Lecture 6 Point and Interval Estimation.pptx
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Point and Interval Estimation: Objectives: Apply the basics of inferential statistics in terms of point estimation. Compute point and estimation of population means and confidence interval. Interpret the results of point and interval estimation. Estimation: Estimating the value of parameter from the sample: An aspect of inferential statistics. Why to estimate: Population is large enough so we can only estimate. Types of estimation: Point Estimation: A specified number value (single value) that is an estimate of a population parameter. The point estimate of the population mean µ is the sample mean. Interval Estimate: Range of values to estimate about population parameter. Confidence Interval Estimation: Range of values to estimate about population parameter. May contain the parameter or not (Degree of confidence). Ranges between two values. Example: Age (in years) 4 BScN students: 20<µ < 25 or (22.5 +2.5) FORMULA: Point estimate (x) + Critical Value x Standard Error. Confidence Interval is a particular interval of estimate. Given that sample size is large, the 95% of the sample means taken from same population and same sample size will fall in + 1.96 SD of the population mean. Three commonly used Confidence Intervals are 90%, 95% (by default) , and 99%. Why not too small or too large confidence intervals? Too wide: 99.9% Interval too broad Too narrow: 80 % More uncertainty to have population mean. The 99% of the sample means taken from same population and same sample size will fall in + 2.575 SD of the population mean. Interpretation: 99% probability that interval will enclose population parameter and 1% chance that it will not have population parameter. Level of confidence: The level of certainty that the interval will have the true population mean. Chances of Error: Chances that the interval will not cater the true parameter. Sum of level of confidence and chances of error =100%
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A.6 confidence intervals
A confidence interval provides a range of values that is likely to include an unknown population parameter, with a specified confidence level. A 95% confidence interval states that if you were to repeat the sampling process numerous times, 95% of the calculated confidence intervals would contain the true population parameter. It does not mean there is a 95% chance that the population parameter falls within the given interval. Larger sample sizes are needed to achieve smaller margins of error or higher confidence levels when estimating population parameters from sample data.
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Name Shakeel Nouman
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Contact # 0332-4462527. 0321-9898767
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sn_gcu@hotmail.com
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Similar a Lecture 6 Point and Interval Estimation.pptx
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- How to calculate and interpret confidence intervals.
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📺Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
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Please Subscribe to this Channel for more solutions and lectures
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Module 7 Interval estimatorsMaster for Business Statistics.docx
Module 7
Interval estimators
Master for Business Statistics
Dane McGuckian
Topics
7.1 Interval Estimate of the Population Mean with a Known Population Standard Deviation
7.2 Sample Size Requirements for Estimating the Population Mean
7.3 Interval Estimate of the Population Mean with an Unknown Population Standard Deviation
7.4 Interval Estimate of the Population Proportion
7.5 Sample Size Requirements for Estimating the Population Proportion
7.1
Interval Estimate of the Population Mean with a Known Population Standard Deviation
Interval Estimators
Quantities like the sample mean and the sample standard deviation are called point estimators because they are single values derived from sample data that are used to estimate the value of an unknown population parameter.
The point estimators used in Statistics have some very desirable traits; however, they do not come with a measure of certainty.
In other words, there is no way to determine how close the population parameter is to a value of our point estimate. For this reason, the interval estimator was developed.
An interval estimator is a range of values derived from sample data that has a certain probability of containing the population parameter.
This probability is usually referred to as confidence, and it is the main advantage that interval estimators have over point estimators.
The confidence level for a confidence interval tells us the likelihood that a given interval will contain the target parameter we are trying to estimate.
The Meaning of “Confidence Level”
Interval estimates come with a level of confidence.
The level of confidence is specified by its confidence coefficient – it is the probability (relative frequency) that an interval estimator will enclose the target parameter when the estimator is used repeatedly a very large number of times.
The most common confidence levels are 99%, 98%, 95%, and 90%.
Example: A manufacturer takes a random sample of 40 computer chips from its production line to construct a 95% confidence interval to estimate the true average lifetime of the chip. If the manufacturer formed confidence intervals for every possible sample of 40 chips, 95% of those intervals would contain the population average.
The Meaning of “Confidence Level”
In the previous example, it is important to note that once the manufacturer has constructed a 95% confidence interval, it is no longer acceptable to state that there is a 95% chance that the interval contains the true average lifetime of the computer chip.
Prior to constructing the interval, there was a 95% chance that the random interval limits would contain the true average, but once the process of collecting the sample and constructing the interval is complete, the resulting interval either does or does not contain the true average.
Thus there is a probability of 1 or 0 that the true average is contained within the interval, not a 0.95 probability.
The interval limits are random variables because the ...
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Assume you need to build a confidence interval for a population mean.docx
Assume you need to build a confidence interval for a population mean within some given situation.
Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation.
Thus, based upon the information provided for each situation below, determine which (
t
-,
z
- or neither) distribution is appropriate.
Then
if
you can use either a t- or z- distribution, give the associated critical value (critical
t
- or
z
- score) from that distribution to reach the given confidence level.
a.
99% confidence
n=150
σ known
population data believed to be very skewed
Appropriate distribution:
Associated critical value:
b.
95% confidence
n=10
σ unknown
population data believed to be normally distributed
Appropriate distribution:
Associated critical value:
c.
90% confidence
n=40
σ
unknown
population data believed to be normally distributed
Appropriate distribution:
Associated critical value:
d.
99% confidence
n=12
σ unknown
population data believed to be very skewed
Appropriate distribution:
Associated critical value:
A student researcher is interested in determining the average (
µ
) GPA of all FHSU students, in order to investigate grade inflation at regional universities.
The data below represent the GPA's of thirty-six randomly selected FHSU students.
2.75
2.55
3.95
1.74
2.66
3.10
2.41
1.57
2.12
3.67
3.56
1.98
4.00
3.21
1.95
3.75
1.45
3.01
2.29
2.66
3.95
2.50
3.88
2.79
2.32
3.44
2.07
0.62
2.72
3.55
3.92
3.41
2.14
1.15
2.75
3.25
a.
How do you know that you will need to construct the confidence interval using a
t
-distribution approach as opposed to a
z
-distribution?
We want to construct the mean value confidence interval for the GPA's with a 90% confidence level.
b.
Determine the best point estimate (average) for the mean GPA.
c.
Determine the critical
t
-value(s) associated with the 95% confidence level.
d.
Determine the margin of error.
e.
Determine the confidence interval.
f.
In a sentence, interpret the contextual meaning of your result to part e above...that is relate the values to this situation regarding the mean GPA's of all FHSU students.
Determine the two chi-squared (
χ
2
) critical values for the following confidence levels and sample sizes.
a.
95% and
n
=30
b.
99% and
n
=20
...
Sample size determination
This document discusses factors to consider when determining sample size for statistical studies. It notes that sample size is usually based on the study's objective and should be stated in the study protocol. Key factors in determining sample size include estimates of population standard deviation, acceptable sampling error levels, and desired confidence levels. Several methods are described for calculating sample size, including traditional statistical models and Bayesian models. The document also discusses concepts like sampling distributions of means and proportions, and factors that affect sample size calculations for estimating proportions, such as specifying acceptable error levels, confidence levels, and population proportion estimates.
Standard Error & Confidence Intervals.pptx
Certainly! Let's delve into the concept of **standard error**.
## What Is Standard Error?
The **standard error (SE)** is a statistical measure that quantifies the **variability** between a sample statistic (such as the mean) and the corresponding population parameter. Specifically, it estimates how much the sample mean would **vary** if we were to repeat the study using **new samples** from the same population. Here are the key points:
1. **Purpose**: Standard error helps us understand how well our **sample data** represents the entire population. Even with **probability sampling**, where elements are randomly selected, some **sampling error** remains. Calculating the standard error allows us to estimate the representativeness of our sample and draw valid conclusions.
2. **High vs. Low Standard Error**:
- **High Standard Error**: Indicates that sample means are **widely spread** around the population mean. In other words, the sample may not closely represent the population.
- **Low Standard Error**: Suggests that sample means are **closely distributed** around the population mean, indicating that the sample is representative of the population.
3. **Decreasing Standard Error**:
- To decrease the standard error, **increase the sample size**. Using a large, random sample minimizes **sampling bias** and provides a more accurate estimate of the population parameter.
## Standard Error vs. Standard Deviation
- **Standard Deviation (SD)**: Describes variability **within a single sample**. It can be calculated directly from sample data.
- **Standard Error (SE)**: Estimates variability across **multiple samples** from the same population. It is an **inferential statistic** that can only be estimated (unless the true population parameter is known).
### Example:
Suppose we have a random sample of 200 students, and we calculate the mean math SAT score to be 550. In this case:
- **Sample**: The 200 students
- **Population**: All test takers in the region
The standard error helps us understand how well this sample represents the entire population's math SAT scores.
Remember, the standard error is crucial for making valid statistical inferences. By understanding it, researchers can confidently draw conclusions based on sample data. 📊🔍
If you need further clarification or have additional questions, feel free to ask! 😊
---
I've provided a concise explanation of standard error, emphasizing its importance in statistical analysis. If you'd like more details or specific examples, feel free to ask! ¹²³⁴
Source: Conversation with Copilot, 5/31/2024
(1) What Is Standard Error? | How to Calculate (Guide with Examples) - Scribbr. https://www.scribbr.com/statistics/standard-error/.
(2) Standard Error (SE) Definition: Standard Deviation in ... - Investopedia. https://www.investopedia.com/terms/s/standard-error.asp.
(3) Standard error Definition & Meaning - Merriam-Webster. https://www.merriam-webster.com/dictionary/standard%20error.
(4) Standard err
GROUP 1 biostatistics ,sample size and epid.pptx
The document discusses sample size determination in epidemiological studies. It defines key terms like sample, sample size, and reasons for determining sample size such as allowing for appropriate analysis and providing an accurate level of precision. Methods for determining sample size discussed include using the entire population (census), published sample sizes, and formulas. Several formulas are provided for estimating sample sizes needed for different study designs like descriptive studies and studies estimating a mean or proportion. Steps for using the formulas are outlined.
Chapter 8
This document discusses confidence intervals for estimating population parameters. It provides examples of constructing point and interval estimates for the population mean and proportion from sample data. Confidence intervals allow us to estimate a range of plausible values for the true population parameter based on the sample results and desired confidence level, rather than just a single point value. The width of the confidence interval depends on the sample size and confidence level, with larger samples and lower confidence levels producing narrower intervals.
Inferential statistics
The document discusses key concepts in statistical inference including estimation, confidence intervals, hypothesis testing, and types of errors. It provides examples and formulas for estimating population means from sample data, calculating confidence intervals, stating the null and alternative hypotheses, and making decisions to accept or reject the null hypothesis based on a significance level.
Chapter 11
To determine the appropriate sample size for quantitative research, key factors must be considered including:
1) The desired level of precision or acceptable margin of error for results.
2) The required confidence level, typically 95%.
3) An estimate of the population variability based on available data.
Using a basic formula that incorporates these factors, the sample size can be computed to achieve the desired precision at the specified confidence level. Probability sampling methods like simple random and stratified sampling are generally most effective when a sampling frame is available.
Quantitative critical appraisal october 2015
This document provides an introduction to critical appraisal of research articles. It explains that critical appraisal assesses the validity, results, and relevance of studies. Key aspects include evaluating study design, interpreting basic statistics and event rates, and determining applicability of results. Ready-made checklists can help appraise different types of research studies. Understanding concepts like confidence intervals, p-values, and risk ratios is important for interpretation. Practice is needed to develop critical appraisal skills.
Inferential statistics.ppt
This document discusses inferential statistics, which uses sample data to make inferences about populations. It explains that inferential statistics is based on probability and aims to determine if observed differences between groups are dependable or due to chance. The key purposes of inferential statistics are estimating population parameters from samples and testing hypotheses. It discusses important concepts like sampling distributions, confidence intervals, null hypotheses, levels of significance, type I and type II errors, and choosing appropriate statistical tests.
Problems related to texts Chapter 7.docx
Problems related to text's Chapter 7:
1.
Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which (
t
-,
z
- or neither) distribution is appropriate. Then
if
you can use either a t- or z- distribution, give the associated critical value (critical
t
- or
z
- score) from that distribution to reach the given confidence level.
a.
99% confidence
n=150
σ known
population data believed to be very skewed
Appropriate distribution:
Associated critical value:
b.
95% confidence
n=10
σ unknown
population data believed to be normally distributed
Appropriate distribution:
Associated critical value:
c.
90% confidence
n=40
σ
unknown
population data believed to be normally distributed
Appropriate distribution:
Associated critical value:
d.
99% confidence
n=12
σ unknown
population data believed to be very skewed
Appropriate distribution:
Associated critical value:
2.
A student researcher is interested in determining the average (
µ
) GPA of all FHSU students, in order to investigate grade inflation at regional universities. The data below represent the GPA's of thirty randomly selected FHSU students.
2.75
2.55
3.95
1.74
2.66
3.10
2.41
1.57
2.12
3.67
3.56
1.98
4.00
3.21
1.95
3.75
1.45
3.01
2.29
2.66
3.95
2.50
3.88
2.79
2.32
3.44
2.07
0.62
2.72
3.55
3.92
3.41
2.14
1.15
2.75
3.25
a.
How do you know that you will need to construct the confidence interval using a
t
-distribution approach as opposed to a
z
-distribution?
We want to construct the mean value confidence interval for the GPA's with a 90% confidence level.
b.
Determine the best point estimate (average) for the mean GPA.
c.
Determine the critical
t
-value(s) associated with the 95% confidence level.
d.
Determine the margin of error.
e.
Determine the confidence interval.
.
inferencial statistics
Dr. Abhay Pratap Pandey introduces statistical inference and its key concepts. Statistical inference allows making conclusions about a population based on a sample. It involves estimation and hypothesis testing. Estimation determines population parameters using sample statistics. Hypothesis testing determines if sample data provides sufficient evidence to reject claims about population parameters. The document defines key terms like population, sample, parameter, statistic, and discusses properties of estimators like unbiasedness and consistency. It also explains hypothesis testing concepts like null and alternative hypotheses, types of errors, and steps to conduct hypothesis tests on a population mean. An example demonstrates hypothesis testing for a population mean using a z-test.
2_Lecture 2_Confidence_Interval_3.pdf
Census
Everyone in population
Eg. All Cambodian residents
Population
is a set of persons (or objects) having a common observable characteristic.
the entire collection of units about which we would like information
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Statistical inference is the process by which we draw conclusions about a population from data collected on a sample.
In medical research
Population
All patients candidate for treatment
Sample
All patients candidate for treatment who volunteer for your study
Infer results from volunteers (sample) to other candidates for the same treatment (population).
We usually obtain information on an appropriate sample of the community and generalize from it to the entire population.
The way the sample is selected, not its size, determines whether we may draw appropriate inferences about a population.
The primary reason for selecting a sample from a population is to draw inferences about that population.
Statistical inference is the process by which we infer
Normal and standard normal distribution
The document discusses normal and standard normal distributions. It provides examples of using a normal distribution to calculate probabilities related to bone mineral density test results. It shows how to find the probability of a z-score falling below or above certain values. It also explains how to determine the sample size needed to estimate an unknown population proportion within a given level of confidence.
2_5332511410507220042.ppt
What is statistical analysis? It's the science of collecting, exploring and presenting large amounts of data to discover underlying patterns and trends. Statistics are applied every day – in research, industry and government – to become more scientific about decisions that need to be made.
Similar a Lecture 6 Point and Interval Estimation.pptx (20)
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Unit 12. Limitations & Recomendations.pptx
Limitations & Recommendations:
Objectives:
Enlist theoretical and methodological/procedural limitation
Discuss the importance of study to give recommendations at organizational, national, international level.
Discussion Section:
The discussion section is where the researcher delve into the meaning, importance, and relevance of results.
It should focus on explaining and evaluating what you found, showing how it relates to your literature review and paper or dissertation topic, and making an argument in support of your overall conclusion. It should not be a second results section.
There are different ways to write this section, but you can focus your writing around these key elements:
Summary:
A brief recap of your key results
Interpretations:
What do your results mean?
Implications:
Why do your results matter?
Limitations:
What can’t your results tell us?
Recommendations:
Avenues for further studies or analyses.
Not to Include in Discussion Section:
There are a few common mistakes to avoid when writing the discussion section of your paper.
Don’t introduce new results: You should only discuss the data that you have already reported in your results section.
Don’t make inflated claims: Avoid over interpretation and speculation that isn’t directly supported by your data.
Don’t undermine your research: The discussion of limitations should aim to strengthen your credibility, not emphasize weaknesses or failures.
Step 1: Summarize your key findings:
Start this section by reiterating your research problem and concisely summarizing your major findings.
Don’t just repeat all the data you have already reported—aim for a clear statement of the overall result that directly answers your main research question.
This should be no more than one paragraph.
Many students struggle with the differences between a discussion section and a results section.
The crux of the matter is that your results sections should present your results, and your discussion section should subjectively evaluate them.
Examples: Summarization sentence starters;
The results indicate that…
The study demonstrates a correlation between…
This analysis supports the theory that…
The data suggest that…
Step 2: Give your interpretations:
The meaning of your results may seem obvious to you, but it’s important to spell out their significance for your reader, showing exactly how they answer your research question.
The form of your interpretations will depend on the type of research, but some typical approaches to interpreting the data include:
Identifying correlations, patterns, and relationships among the data
Discussing whether the results met your expectations or supported your hypotheses
Contextualizing your findings within previous research and theory
Explaining unexpected results and evaluating their significance
Considering possible alternative explanations and making an argument for your position.
Unit 11. Interepreting the Research Findings.pptx
INTERPRETING THE RESEARCH FINDINGS.
Objectives:
At the completion of this unit learners will be able to
Discuss the different means and interpretation of data presentation/displaying through, Graphs (pie, bar, line, histogram), Tables, Charts. (spot map)
Discuss the different inferences through inferential tests and their interpretation.
Methods of Data collection and Presentation:
Methods of data collection:
Source of Data:
Statistical data may be obtained from two sources, namely, primary and secondary.
Primary data:
data measured or collected by the investigator or the user directly from the source. Primary sources are sources that can supply first hand information for immediate user.
Secondary data:
When an investigator uses data, which have already been collected by others, such data are called secondary data. Data gathered or compiled from published and unpublished sources.
Two different methods of collecting data:
Extraction of data from self – administered questionnaire
Direct investigation-measurement (observation) of the subject and interviewing (face-to-face, telephone)
first step is to decide on which of these three methods to use.
Methods of data Presentation:
Textual Method: – a narrative description of the data gathered.
Tabular Method or frequency distribution :– a systematic arrangement of information into columns and rows.
Graphical Method :– an illustrative description of the data.
The frequency distribution table:
A statistical table showing the frequency or number of observations contained in each of the defined classes or categories.
Frequency distribution: is a basic techniques that provide rich insights into the data and lay the foundation for more advanced analysis.
A frequency distribution table: lists categories of scores along with their corresponding frequencies.
Frequency distribution:
It is a grouping of all the (numerical) observations into intervals or classes together with a count of the number of observations that fall in each interval or class.
A frequency distribution has two main parts:
The values of the variable (if quantitative) or the categories (if qualitative), and
The number of observations (frequency) corresponding to the values or categories.
There are two types of Frequency distributions:
Categorical (or qualitative) Numerical (or quantitative)
Categorical Frequency Distribution:
Data are classified according to non-numerical categories. Categories must be mutually exclusive.
Used to present nominal and ordinal data
Nominal data: Here the construction is straight forward: count the occurrences in each category and find the totals.
Example: The martial status of 60 adults classified as single, married, divorced and widowed is presented in a FD as below:
Ordinal data:The construction is identical to the nominal case. How ever, the categories should be put in an ordered manner
Example: Satisfaction of hospital admission in a hospital size of 80 is presented as.
Unit 10. Data Collection & Analysis.pptx
Data Collection & Data Analysis:
Objectives:
Discuss the term data collection and various ways of data collection, including training of data collectors
Discuss the types of data and various methods of data collection.
Run the statistical software for quantitative, qualitative and outcome research.
Know the salient features of data entry and analysis soft wares, i.e SPSS and NVIVO
Apply appropriate statistical test.
Data Collection:
“The process of gathering and measuring information on variables of interest, in an established systematic fashion that enables one to answer queries, stated research questions, test hypotheses, and evaluate outcomes.”
Data Collection Sources:
Primary
Secondary
Interviews:
The researcher asks questions of a large sampling of people, either by direct interviews or means of mass communication such as by phone or mail. This method is by far the most common means of data gathering.
Projective Data Gathering:
Projective data gathering is an indirect interview, used when potential respondents know why they're being asked questions and hesitate to answer.
For instance, someone may be reluctant to answer questions about their phone service if a cell phone carrier representative poses the questions. With projective data gathering, the interviewees get an incomplete question, and they must fill in the rest, using their opinions, feelings, and attitudes.
Delphi Technique:
The Oracle at Delphi, according to Greek mythology, was the high priestess of Apollo’s temple, who gave advice, prophecies, and counsel. In the realm of data collection, researchers use the Delphi technique by gathering information from a panel of experts. Each expert answers questions in their field of specialty, and the replies are consolidated into a single opinion.
Focus Groups:
Focus groups, like interviews, are a commonly used technique. The group consists of anywhere from a half-dozen to a dozen people, led by a moderator, brought together to discuss the issue.
Questionnaires:
Questionnaires are a simple, straightforward data collection method. Respondents get a series of questions, either open or close-ended, related to the matter at hand.
Secondary Data Collection.
Unlike primary data collection, there are no specific collection methods. Instead, since the information has already been collected, the researcher consults various data sources, such as:
Financial Statements
Sales Reports
Retailer/Distributor/Deal Feedback
Customer Personal Information (e.g., name, address, age, contact info)
Business Journals
Government Records (e.g., census, tax records, Social Security info)
Trade/Business Magazines
The internet.
Qualitative data analysis:
Qualitative data is analyzed via two approaches:
Thematic Analysis (Braun & Clarke 2006)
Content Analysis (Creswell 2013)
Unit 9c. Data Collection tools.pptx
Data Collection Tools: Validity & Reliability.
Objectives:
Discuss types of measurement tools for collecting data for quantitative, qualitative and outcome research.
Differentiate between interview guide and interview schedule
Discuss reliability and validity of questionnaires.
Data:
The set of values collected for the variable of each of the elements belonging to the sample
Data sources include (Quantitative)
Surveys where there are a large number of respondents (esp where you have used a Likert scale)
Questionnaires, data collection tools/ instruments
Observations (counts of numbers and/or coding data into numbers)
Secondary data (government data; SATs scores etc)
Analysis techniques include hypothesis testing, correlations and cluster analysis.
Data sources include (Qualitative)
Interviews (structured, semi-structured or unstructured)
Focus groups
Questionnaires or surveys
Secondary data, including diaries, self-reporting, written accounts of past events/archive data and company reports;
Direct observations – may also be recorded (video/audio)
Ethnography
Data analysis; thematic or content analysis .
Data Collection:
“The process of gathering and measuring information on variables of interest, in an established systematic fashion that enables one to answer queries, stated research questions, test hypotheses, and evaluate outcomes.”
Data Collection Methods:
Surveys, quizzes, and questionnaires
Interviews
Focus groups
Direct observations
Documents and records.
Data Collection Tools for Quantitative Research:
Closed-ended Surveys and Online Quizzes
Closed-ended surveys and online quizzes are based on questions that give respondents predefined answer options to opt for. There are two main types of closed-ended surveys – those based on categorical and those based on interval/ratio questions.
Categorical survey questions can be further classified into dichotomous (‘yes/no’), multiple-choice questions, or checkbox questions and can be answered with a simple “yes” or “no” or a specific piece of predefined information.
Interval/ratio questions, on the other hand, can consist of rating-scale, Likert-scale, or matrix questions and involve a set of predefined values to choose from on a fixed scale.
Data Collection Tools for Qualitative Research:
1. Open-Ended Surveys and Questionnaires
Opposite to closed-ended are open-ended surveys and questionnaires. The main difference between the two is the fact that closed-ended surveys offer predefined answer options the respondent must choose from, whereas open-ended surveys allow the respondents much more freedom and flexibility when providing their answers.
2. In-depth Interviews/ Face to Face Interviews
One-on-one (or face-to-face) interviews are one of the most common types of data collection methods in qualitative research. Here, the interviewer collects data directly from the interviewee.
Unit 9b. Sample size estimation.ppt
Sample size Calculation:
Objectives:
Calculate sample size according to particular type of research, and purpose.
Identify and select various software to calculate sample size according to particular type of research, and purpose.
Why to calculate sample size?
To show that under certain conditions, the hypothesis test has a good chance of showing a desired difference (if it exists)
To show to the IRB committee and funding agency that the study has a reasonable chance to obtain a conclusive result
To show that the necessary resources (human, monetary, time) will be minimized and well utilized.
Most Important: sample size calculation is an educated guess
It is more appropriate for studies involving hypothesis testing
There is no magic involved; only statistical and mathematical logic and some algebra
Researchers need to know something about what they are measuring and how it varies in the population of interest.
SAMPLE SIZE:
How many subjects are needed to assure a given probability of detecting a statistically significant effect of a given magnitude if one truly exists?
POWER:
If a limited pool of subjects is available, what is the likelihood of finding a statistically significant effect of a given magnitude if one truly exists?
Before We Can Determine Sample Size We Need To Answer The Following:
1. What is the primary objective of the study?
2. What is the main outcome measure?
Is it a continuous or dichotomous outcome?
3. How will the data be analyzed to detect a group difference?
4. How small a difference is clinically important to detect?
5. How much variability is in our target population?
6. What is the desired and ?
7. What is the anticipated drop out and non-response % ?
Where do we get this knowledge?
Previous published studies
Pilot studies
If information is lacking, there is no good way to calculate the sample size.
Type I error: Rejecting H0 when H0 is true
: The type I error rate.
Type II error: Failing to reject H0 when H0 is false
: The type II error rate
Power (1 - ): Probability of detecting group difference given the size of the effect () and the sample size of the trial (N).
Estimation of Sample Size by Three ways:
By using
(1) Formulae (manual calculations)
(2) Sample size tables or Nomogram
(3) Softwares.
SAMPLE SIZE FOR ADEQUATE PRECISION:
In a descriptive study,
Summary statistics (mean, proportion)
Reliability (or) precision
By giving “confidence interval”
Wider the C.I – sample statistic is not reliable and it may not give an accurate estimate of the true value of the population parameter.
Sample size calculation for cross sectional studies/surveys:
Cross sectional studies or cross sectional survey are done to estimate a population parameter like prevalence of some disease in a community or finding the average value of some quantitative variable in a population.
Sample size formula for qualitative variable and quantities variable are different.
Unit 9a. Sampling Techniques.pptx
Samples, Sampling measurement tools, Instruments:
Objectives:
1. Define the term population sample and sampling.
2. Calculate sample size according to particular type of research, and purpose.
3. Identify and select various software to calculate sample size according to particular type of research, and purpose.
4. Discuss types of measurement tools for collecting data from quantitative, qualitative and outcome research.
5. Differentiate between interview guide and interview schedule
6. Discuss reliability and validity of questionnaires
7. Establish reliability and validity of questionnaires
Definitions:
Population vs. Sample
Population
The set of all the measurements of interest to the investigator.
Monthly income of households in Pakistan
Number of TB Patients in Pakistan
All the patients visited emergency of the ABC Hospital in the year 2014
Neonatal mortality in Pakistan.
Sample
It is a group of subjects selected from a population
A random sample is a good representative of population
Example
A survey of 1,000 households taken from all parts of Pakistan to assess their monthly income.
Parameter vs. Statistics:
Parameter
– The characteristics of interest to the researcher in the population is called a parameter.
E.g. average household size and percent of households with modern sanitation as reported in the 1998 census of Karachi
Statistic
– The characteristics of interest to the researcher in the sub-set of population is called a statistic.
E.g. average household size and percent of households as reported from a sample survey of 6,000 households in Karachi, 2010.
Examples:
Parameter:
Average monthly income of households in Pakistan
Proportion of households in Karachi who have at least one special child at their residence
Prevalence of COVID 19 in Pakistan
Statistic:
If taken from a sample each one of above is called statistic.
Sampling:
A process of selecting units (e.g., people, organizations) from a population of interest so that by studying the sample may fairly generalize results back to the population from which they were chosen.
Types of Sampling Plans:
Probability Sampling:
Simple random sampling
Systematic sampling
Stratified sampling
Cluster sampling
Multi-stage sampling
Simple Random Sampling:
In simple random sampling, every subject has an equal chance of being selected for the study.
Individuals who make up the subset of the larger group are chosen at random, each individual in the large population set has the same probability of being selected.
Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100. If the population is less than 100 then you really need to survey all of them.
Random sampling is used in science to conduct randomized control tests or for blinded experiments.
Approaches in Simple Random Sampling:
Method of lottery
Using the lottery method is one of the oldest ways and is a mechanical example of random sample.
Unit 8. Ethical Considerations in Reseaerch.pptx
Ethical Consideration in Research:
Objectives:
1. Define the terms related to ethics in research
2. Discuss historical events of ethical mischiefs and evolution of ethics as protecting human rights
3. Discuss the ethical principles, declaration of Helsinki and research code of ethics
4. Describe different types of informed consent, i.e. verbal, written, individual and institutional consent.
5. Produce a meaningful informed consent form.
6. Identify role and importance of ethical considerations in research.
Ethical Considerations in Research:
Ethical considerations in research are a set of principles that guide the research designs and practices.
Scientists and researchers must always adhere to a certain code of conduct when collecting data from people.
The goals of human research often include understanding real-life phenomena, studying effective treatments, investigating behaviors, and improving lives in other ways.
What you decide to research and how you conduct that research involve key ethical considerations.
Ethical considerations work to:
Protect the rights of research participants
Enhance research validity
Maintain scientific or academic integrity.
History of Research Ethics:
Nuremberg Code
Dec. 9, 1946, when an American military tribunal opened criminal proceedings against 23 leading German physicians and administrators for their willing participation in war crimes and crimes against humanity.
Among the charges were that German physicians conducted medical experiments on thousands of concentration camp prisoners without their consent. Most of the subjects of these experiments died or were permanently crippled as a result.
As a direct result of the trial, the Nuremberg Code was established in 1948, stating that “The voluntary consent of the human subject is absolutely essential,” making it clear that subjects should give consent and that the benefits of research must outweigh the risks.
Although it did not carry the force of law, the Nuremberg Code was the first international document which advocated voluntary participation and informed consent.
Thalidomide
In the late 1950s, thalidomide was approved as a sedative in Europe; it was not approved in the United States by the FDA.
The drug was prescribed to control sleep and nausea throughout pregnancy, but it was soon found that taking this drug during pregnancy caused severe deformities in the fetus.
Many patients did not know they were taking a drug that was not approved for use by the FDA, nor did they give informed consent. Some 12,000 babies were born with severe deformities due to thalidomide.
U.S. Senate hearings followed and in 1962 the so-called “Kefauver Amendments” to the Food, Drug, and Cosmetic Act were passed into law to ensure drug efficacy and greater drug safety.
For the first time, drug manufacturers were required to prove to the FDA the effectiveness of their products before marketing them.
Unit 7. Theoritical & Conceptual Framework.pptx
THEORETICAL AND CONCEPTUAL FRAMEWORKS:
objectives:
1. Discuss the different types of models and frameworks used in research framework
2. Discuss the use of theoretical/conceptual frameworks and models in the research.
3. Differentiate theoretical/conceptual frameworks and models
4. Recognize the best suit theory or theoretical model/framework for particular research study
5. Develop conceptual models/framework, best suit for particular research study.
What is a theoretical framework?
A theoretical framework is a summary of the researcher’s theory regarding a particular problem that is developed through a review of previously tested knowledge of variables involved. It identifies a plan for investigation and interpretation of the findings.
It relates to philosophical basis on which the research takes place and form the link between the theoretical aspects and practical components of the investigation undertaken. Therefore it’’ has implications for every decision made in the research process".
Theoretical framework can be considered as a conceptual model that establishes a sense of structure that guides the research process. It includes the variables a researcher intends to measure and relationships he/she seeks to understand. Essentially, this is where a researcher develops a “theory” and build his/her case for investigating that theory.
The theoretical framework is the researcher’s presentation of a theory that explains a particular problem and it is not based on his/her suspicions alone.
Theoretical framework is presented in the early section of a dissertation mainly in chapter two of the report and provides the rationale for conducting your research to investigate a particular research problem.
It involves a well-supported rationale and is organized in a manner that helps the reader understand and asses the perspective of the researcher.
When developing a theoretical framework:
The researcher start by describing what is known about the variables involved, what is known about their relationship, and what can be explained thus far.
One need to investigate other researchers’ theories behind these relationships and identify a theory (or a combination of theories) that explain his/her major research problem.
The researcher need to consider alternative theories that might challenge his/her perspective.
One also considers the limitations associated with his/her theory and quite possibly that problem could be better understood by other theoretical frameworks.
Significance of a theoretical framework:
It helps the researcher to consider other possible frameworks and to reduce biases that may sway the researcher’s interpretation.
It clarifies researcher’s implicit theory in a manner that is more clearly defined.
It demonstrates that the relationships proposed by the researcher are not based on his/her personal instincts or guesses, but rather formed from facts obtained from authors of previous research.
Unit 6. Literature Review & Synthesis.pptx
Literature Review:
Objectives:
Define literature review and related terms
Identify theoretical and empirical literature and their resources
Locate search engines and literature data bases like Cochrane, CINHAL, PubMed etc
Utilize data bases by retrieving required data
Identify framework to synthesize and organize the literature, such as traditional hierarchy/level of evidence.
INTRODUCTION:
It is one of the most important steps in research process. It is an account of what is already known about particular phenomenon.
The main purpose is to convey to the readers about the work already done and knowledge and ideas that have been already established on a particular topic of research.
DEFINITION:
It is a body of text that aims to review the critical points of knowledge on a particular topic of research.
It is an account of what has been already established or published on a particular research topic by accredited scholars and researchers.
IMPORTANCE:
Identification of research problem and refinement of research questions
Generation of useful research questions or projects
Orientation of what is known and not known about an area of inquiry
Determine any gaps in the body of knowledge
Discovery of unanswered questions about subjects, concepts or problems.
Identification of relevant conceptual framework
Identification of development of new or redefined clinical intervention
Development of hypothesis to be tested in research instruments
Helps in planning the methodology of present study.
PURPOSES:
Describe the relationship of each study to other research study under consideration.
Identify new ways to interpret on any gaps in previous research
Resolve conflicts amongst seemingly contradictions previous studies
Identify areas of prior scholarship to prevent duplication of effort.
See what has and has not been investigated
Identify potential relationships between concepts and identify researchable hypothesis
Develop alternative research projects
Learn how others have defined and measured key concepts.
SOURCES:
Primary Sources:
Literature review mostly relies on primary source (i.e) research reports, which are description of studies written by researchers who conducted them. Primary source is written by a person who developed the theory or conducted the research or is the description of an investigation written by the person who conducted it.
Secondary Sources:
Secondary source research documents or description of studies prepared by someone other than the original research.
Main sources:
Electronic database
Books
Journals
Conference Papers
Theses
Encyclopedia and Dictionary
Research Reports
Magazines and Newspaper.
Databases:
CINAHL (Cumulative Index to Nursing and Allied Health Literature)
MEDLINE (Medical Literature Analysis and Retrieved System Online)
PUBMED
Medline Plus
Education Resource Information Center
British Nursing Index
Web of Science
Science Direct
Google Scholar.
Unit 5. Research Question and Hypothesis.pptx
Research Question and Hypothesis:
Objectives:
Identify variables in the study, to formulate research question and hypothesis
Formulate research question, which is to be answered statistically and logically
Formulate null hypothesis and test able research hypothesis, which is to be answered statistically.
Explore and select the appropriate statistical measures for selected research question
Justify the appropriateness of selected statistical test, chosen for the testing question and hypothesis
Interpret the selected statistical test, chosen for the testing question and hypothesis in statistical manner
Inference the selected statistical test, chosen for the testing question and hypothesis in statistical manner.
Variable:
A characteristic, attribute of a person or object that differs among the persons or object being studied (eg. Age, sex, blood type etc.)
Classification of research variables:
One variable study/ univariate study
“what sources of work stress are identified by thoracic care unit nurses?”
Two variables study/bivariate study
One is dependent and the other is independent
Ex. Is there a correlation between the number of sources of stress reported by nurses in a thoracic intensive care. The independent variable is “ the number of reported sources of stress.” and the dependent variable is the desire to leave to leave employment in the thoracic intensive care unit.”
Multi-variables study/ multivariate study
More than two variables are examined in a study
Ex. Why clients do not take their medications as directed after they are discharged?
Why do nursing students pass/fail the examination?
Types of Variables:
Independent variable
The “cause” or the variable thought to influence the dependent variable in experimental research it is the variable manipulated by the researcher.
Dependent variable
The “effect” a response or behavior that is influenced by the independent variable; sometimes called criterion variable.
Intervening variables
Comes between dependent and independent variable
Extraneous variable
Influence can be change
Dichotomous variable
Two choice or result (male/female)
Polychotomous variables
Multiple variables
Research Question:
Specific question that the researcher expects to be answered in a study.
Should specify the variables and the population that are being studied
Example;
“Is there a difference in anxiety levels of women about to undergo hysterectomy between those women who receive a back rub and those who not receive a back rub?”
Formulating a Research Question:
Research questions for studies that examine more than one variable are usually written as correlational statement or comparative statement.
1. Correlational Statement
(dependent and independent)
“ Is there a correlation between anxiety and midterm scores of baccalaureate nursing students?”
Unit 4. Research Problem, Purpose, Objectives, Significance and Scope..pptx
Research Problem, Purpose, Objectives, Significance and Scope:
Objectives:
1. Identify the interest area of research
2. Discuss the problem statement and research purpose
3. Develop objectives of research
4. Elaborate on significance and scope of the research
5. Differentiate between significance and scope of the research.
Research Proposal:
A research proposal describes what you will investigate, how will you carry out your research, and why the research is essential to be conducted.
It should be noted that the proposal acts as an introduction of a thesis/dissertation or a project report.
The proposal helps the researcher to think practically and to be on the right track during the research process.
Almost all students who intend to write Bachelor’s, Master, or Ph.D. thesis/dissertation or those who intend to apply for scholarships or research grants, need to write a research proposal.
Attributes of Good Research Proposal:
It is innovative and contains impressive research idea(s).
The research questions and objectives are clear.
The methodology and data sources are well known.
The significance of the study is justified.
The objectives of the study could be met within the timeline.
The writing style is clear and concise, and there is no ambiguity.
There is no contradiction in objectives, research questions, and methodology.
The budget and the proposal narrative are consistent.
Contents of the Thesis/Dissertation Proposal:
Title of Study
Abstract
Introduction
Significance of the Study
Research Questions
Research Objectives
Research Hypothesis
Review of Literature
Methodology
Data Sources
Tentative Table of Content of Thesis
References.
Title of Study:
It should be appealing and meaningful.
It should not be a single word.
It should be short and self-explanatory.
It should reflect the study properly.
It should not be a conclusion.
It should not be contradictory to the methodology.
Abstract:
It motivates the reader to read the full text.
It is a brief overview of the proposal, consisting of 100 to 300 words.
It summarizes the essential elements of the research proposal.
It may not cite the existing relevant literature.
It may summarize the methods, results, and implications.
Introduction:
It highlights the nature of the problem.
It discusses the background of the problem.
It explains the current situation of the problem.
It discusses the significance of the study.
It states the research question(s) and the research objectives of the study.
It mentions the limitations of the study (if any).
It explains the structure of the study.
Identify the interest area of research:
Clinical Practice
Nursing Education
Community/ Public Health
Literature Review
Theories
Research Priorities
Peer Interaction.
Unit 3. Outcome Reseaerch.pptx
Introduction to Outcome Research
Objectives:
1. Define the terms related to outcome research
2. Discuss basis of outcome research with relation to Donabedian‟s theory.
3. Describe methods/approaches/types of outcome research.
4. Understand methodologies of outcome research.
Outcome Research:
Outcomes research is a broad umbrella term without a consistent definition.
It tends to describe research that is concerned with the effectiveness of public-health interventions and health services; that is, the outcomes of these services.
Aimed at assessing the quality and effectiveness of health care as measured by the attainment of a specified end result or outcome.
Measures include parameters such as improved health, lowered morbidity or mortality, and improvement of abnormal states (such as elevated blood pressure).
Theoretical Basis of Outcomes Research:
The theorist Avedis Donabedian (1966) proposed a theory of quality health care and the process of evaluating it.
The three dimensions of the model are health, subjects of care, and providers of care.
The concept of health has Three aspects; Physical-physiological function, Psychological function, and Social function.
The concept subjects of care has two primary aspects: patient and person.
A patient is defined as someone who has already gained access to some care, and a person as someone who may or may not have gained access to care.
Each of these concepts is further categorized by the concepts individual and aggregate.
Within patient, the aggregate is a caseload; within person, the aggregate is a target population or a community.
The concept providers of care shows levels of aggregation and organization of providers.
The first level is the individual practitioner. At this level, consideration is given to the individual provider rather than others who might be involved in the subject’s care, whether individual or aggregate.
As the levels progress, providers of care include several practitioners, who might be of the same profession or different professions and “who may be providing care concurrently, as individuals, or jointly, as a team”.
At higher levels of aggregation, the provider of care is institutions, programs, or the healthcare system as a whole.
The essence of Donabedian’s framework is the physical-physiological function of the individual patient being cared for by the individual practitioner. Examining quality at this level is relatively simple.
When more than one practitioner is involved, both individual and joint contributions to quality must be evaluated.
Concepts such as coordination and teamwork must be conceptually and operationally defined. When a person is the subject of care, an important attribute is access.
When an aggregate is the subject of care, an important attribute is resource allocation. Access and resource allocation are interrelated, because they each define who gets care, the kind of care received, and how much care is received.
Unit 2. Introduction to Quantitative & Qualitative Reseaerch.pptx
Introduction to Quantitative and Qualitative Research:
Objectives:
Define the terms of qualitative and quantitative research.
2. Differentiate between qualitative and quantitative research.
3. Describe methods/approaches/types of quantitative research, i.e. Descriptive, Co- relational, Quasi-Experimental and Experimental research.
4. Describe methods/approaches/types of qualitative research i.e. Phenomenological, Grounded Theory, Ethnographical, and Historical research
5. Understand methodologies of qualitative and quantitative research.
Quantitative Research:
Attempts to explain phenomena by collecting and analyzing numerical data
Tells if there is a “difference” but not necessarily why
Data collected are always numerical and analysed using statistical methods
Variables are controlled as much as possible (RCTs as the gold standard) so could eliminate interference and measure the effect of any change
Randomisation to reduce subjective bias
If there are no numbers involved, its not quantitative
Some types of research lend themselves better to quant approaches than others.
Quantitative data:
Data sources include
Surveys where there are a large number of respondents (esp where you have used a Likert scale)
Questionnaires, data collection tools/ instruments
Observations (counts of numbers and/or coding data into numbers)
Secondary data (government data; SATs scores etc)
Analysis techniques include hypothesis testing, correlations and cluster analysis.
Qualitative Research:
Any research that doesn’t involve numerical data
Instead uses observations, words, pictures, videos, audio recordings. Field notes, expressions, and peoples’ own words.
Tends to start with a broad question rather than a specific hypothesis
Develop theory rather than start with one
Tends to yield rich data to explore how and why things happened
Don’t need large sample sizes (in comparison to quantitative research).
Qualitative data:
Interviews (structured, semi-structured or unstructured)
Focus groups
Questionnaires or surveys
Secondary data, including diaries, self-reporting, written accounts of past events/archive data and company reports;
Direct observations – may also be recorded (video/audio)
Ethnography
Data analysis; thematic or content analysis .
Descriptive Studies:
Describe only; do NOT examine associations between Exposure (E) and health Outcome (O).
Generally the purpose is to describe the variability in a health outcome and/or formulate hypotheses.
A descriptive study involves describing the characteristics of a particular situation event or case.
Descriptive studies can be carried out on a small or larger scale.
Case Study :
A study of one diseased individual, providing a detailed description of an uncommon disease; provides timely or rare information.
Case Series :
A study of multiple occurrences of unusual cases that have similar characteristics.
Investigators can calculate the frequency of symptoms or characteristics of people with the disease.
Unit I. Introduction to Nursing Research.pptx
Introduction to Nursing Research:
Objectives:
Define nursing research
Describe ways of knowing in nursing (tradition, authority, borrowing, trial and error, intuition, and research )
Identify role of a nurse in research as ADN, BS, MS, PhD, and DNP
Explain Evidence Based Practice through research.
Definitions:
Research: It is a systematic, formal, rigorous, and precise process used to gain solutions to problems or discover and interpret new facts and relationships.
Nursing Research: is systemic inquiry designed to develop knowledge about issues of importance to nurses, including nursing practice, nursing education, and nursing administration.
Research-based Practice: using research findings to inform the decisions, actions, and interaction of nurses with clients.
Importance of research in nursing:
Emphasizing on the development and utilization of nursing knowledge, which is essential for continued improvement in patient care.
Nurses' need to document the effectiveness of their practices not only to the profession, but also to the clients, administrators, and other professionals. - (Thus research findings help them to eliminate nursing actions that do not achieve desired outcomes or to identify the practices that alter health care outcomes and contain costs).
Nurses' need for understanding the varied dimensions of their profession, (theoretical, ethical, practical dimensions, etc.)
4. Research enables nurses to describe:
The characteristics of a particular nursing situation about which little is known.
Explain phenomena that must be considered in planning nursing care.
Predict the probable outcomes of certain nursing decisions.
Control the occurrence of undesired outcomes.
Initiate activities to promote desired client behavior.
Roles of nurses in nursing research:
It is every nurse's responsibility to engage in one or more roles along the research participation:
Indirect participation:
This is a minimum nurse involvement in a research responsibility. It is done when a nurse read a research report to keep up-to-date on relevant findings that may affect their practice. This level is called "research utilization".
Research Utilization: "Is the use of the research findings in a practice setting"
2. Direct participation: in which nurses are nursing research producers. They are actively participating in designing and implementing research studies.
3. Between these two dimensions of research participation, there are a variety of roles for nurses to play, from these roles:
Attending research presentations at professional conferences.
Evaluating completed research for its possible use in practice.
Discussing the implications and relevance of research findings with clients.
Giving clients information and advice about participation in studies.
Assisting in the collection of research information.
Lecture 14. ANOVA.pptx
Analysis of Variance ANOVA (F test):
It is the method of testing and comparing three or more means.
It is an extension of t test for two independent samples.
ASSUMPTIONS:
The populations from which the samples were obtained must be normally or approximately normally distributed.
The samples must be independent of each other.
The variances of the population must be equal.
SOURCES OF VARIABILITY:
Total variation among scores
Within group Variation
Between group Variation
Sample size need not to be equal
Its always right tail
Lecture 13 Regression & Correlation.ppt
Objectives:
Draw a scatter plot for a set of ordered pairs.
Compute the correlation coefficient.
Test the hypothesis H0: ρ = 0.
Compute the equation of the regression line.
Introduction:
In addition to hypothesis testing and confidence intervals, inferential statistics involves determining whether a relationship between two or more numerical or quantitative variables exists.
Correlation is a statistical method used to determine whether a linear relationship between variables exists.
Regression is a statistical method used to describe the nature of the relationship between variables—that is, positive or negative, linear or nonlinear.
Correlation coefficient, is a numerical measure to determine whether two or more variables are related and to determine the strength of the relationship between or among the variables.
In a simple relationship, there are two variables: an independent variable (predictor variable) and a dependent variable (response variable).
The stronger the relationship is between variables, the more accurate the prediction is.
Scatter Plots and Correlation:
A scatter plot is a graph of the ordered pairs (x, y) of numbers consisting of the independent variable x and the dependent variable y.
Correlation:
The correlation coefficient computed from the sample data measures the strength and direction of a linear relationship between two variables.
The symbol for the sample correlation coefficient is r. The symbol for the population correlation coefficient is .
The range of the correlation coefficient is from 1 to 1.
If there is a strong positive linear relationship between the variables, the value of r will be close to 1.
If there is a strong negative linear relationship between the variables, the value of r will be close to 1.
Possible Relationships Between Variables:
When the null hypothesis has been rejected for a specific a value, any of the following five possibilities can exist.
There is a direct cause-and-effect relationship between the variables. That is, x causes y.
There is a reverse cause-and-effect relationship between the variables. That is, y causes x.
The relationship between the variables may be caused by a third variable.
There may be a complexity of interrelationships among many variables.
The relationship may be coincidental.
Regression:
If the value of the correlation coefficient is significant, the next step is to determine the equation of the regression line which is the data’s line of best fit.
Best fit means that the sum of the squares of the vertical distance from each point to the line is at a minimum.
Procedure Table:
Step 1: Make a table with subject, x, y, xy, x2, and y2 columns.
Step 2: Find the values of xy, x2, and y2. Place them in the appropriate columns and sum each column.
Step 3: Substitute in the formula to find the value of r.
Step 4: When r is significant, substitute in the formulas to find the values of a and b for the regression line equation y = a + bx.
Lecture 12 Chi-Square.pptx
OBJECTIVES:
Recognize the differences between categorical data and continuous data
Discuss assumptions of chi square distribution
Correctly interpret and use the terms:
chi-square test of independence,
contingency table
degrees of freedom,
“2x2” and “r x c” table.
Calculate expected numbers of the cells of a contingency table .
Calculate chi-square test statistic and its appropriate degrees of freedom.
Refer the chi-square table to obtain tabulated value.
Categorical variables take on values that are names or labels, such as ethnicity (e.g., Sindhi, Punjabi, Balochi etc.) and methods of teaching (e.g. lecture, discussion, activity based etc.)
Quantitative variables are numerical. They represent a measurable quantity. For example, the number of students taking Biostatistics Supplementary classes .
CHI-SQUARE TEST:
It is used to determine whether there is a significant association between the two categorical variables from a single population.
CHI-SQUARE DISTRIBUTION PROPERTIES:
As the degrees of freedom increases, the chi-square
curve approaches a normal distribution
It has many shapes which are based on its degree of freedom (df)
Distribution is skewed to the right
A chi-square distribution takes positive values only.
Commonly used approaches are:
Test for independence
Test of homogeneity
CHI-SQUARE TEST OF INDEPENDENCE:
A chi-square test of independence is used when we want to see if there is a relationship/association between two categorical variables.
EXAMPLES OF RELATIONSHIPS
BETWEEN QUALITATIVE VARIABLES:
Qualitative variables are either ordinal or nominal.
Examples:
Do the nurses feel differently about a new postoperative procedure than doctors?
Preference (Old/New) Subjects (Nurses/ Doctors)
Is there any relationship between Soya Use & Lung cancer?
Soya Intake (yes/no) Lung cancer (yes/no)
Is there any relationship between parent’s and their children Children’s Education (Illiterate/Up to Intermediate/Graduate)
education?
Parent’s Education (Illiterate/Up to Intermediate/Graduate)
CONTINGENCY TABLE:
The table which classifies categories of the qualitative
variable.
The number of individuals or items assigned to each category is called the frequency.
WHAT INFORMATION DOES CONTINGENCY TABLE REVEAL?
When we consider two categorical variables at a time, then an observation will belong to a particular category of variable one as well as a particular category of variable two. This type of table is referred as contingency table.
The simplest form of contingency table is a 2x2 contingency table with both
variables having exactly two categories.
WHAT OTHER INFORMATION DOES
CONTINGENCY TABLE REVEAL?
In this table Two independent categorical variables that
form a “r x c” contingency table, where “r” is the number of rows (number of categories in first variable e.g. helmet used at the time of accident or not?) and “c” is the number of columns (number of categories in the second variable e.g. got severe brain injury.
Lecture 11 Paired t test.pptx
OBJECTIVES:
Run the test of hypothesis for mean difference using paired samples. Construct a confidence interval for the difference in population means using paired samples.
Observation of interest will be the difference in the readings
before and after intervention called paired difference observation.
Paired t test:
A paired t-test is used to compare two means where you have two samples in which observations in one sample can be paired with observations in the other sample.
Examples of where this might occur are:
Before-and-after observations on the same subjects (e.g. students’ test
results before and after a particular module or course).
A comparison of two different methods of measurement or two different treatments where the measurements/treatments are applied to the same subjects (e.g. blood pressure measurements using a sphygmomanometer and a dynamap).
When there is a relationship between the groups, such as identical twins.
This test is concerned with the pair-wise differences
between sets of data.
This means that each data point in one group has a related data point in the other group (groups always have equal numbers).
ASSUMPTIONS:
The sample or samples are randomly selected
The sample data are dependent
The distribution of differences is approximately normally
distributed.
Note: The under root is onto the entire numerator and denominator, so you should take the root after solving it entirely
where “t” has (n-1) degrees of freedom and “n” is
the total number of pairs.
Lecture 10 t –test for Two Independent Samples.pptx
This document provides an overview and examples of conducting independent samples t-tests. It begins with explaining the assumptions and steps to conduct an independent samples t-test, including defining the null and alternative hypotheses, significance level, test statistic, critical region, and conclusion. It then provides three examples demonstrating how to apply these steps to compare the mean serum creatinine levels between different groups of patients. The document concludes with explaining how to compute a confidence interval for the difference between two independent means.
Lecture 9 t-test for one sample.pptx
Objectives:
Generate of t-test.
Learn about the assumptions of t-test.
Calculate t-test.
Construct the confidence interval for the population mean.
Recall steps for z test:
1. State null and alternative hypothesis.
2. Determine the level of significance
3. Apply test statistics.
4. Identify critical region/ p-value.
5. Interpret the result.
Need of t test:
When population standard deviation is known or sample is large enough that sample population deviation will represent population’s standard deviation. We can used z-test or standard normal distribution.
What do we do if population standard deviation is not known and the sample size is less than 30?
T distribution:
Also known as student’s test.
Identified by William Goset.
Similarities between z and t distribution:
Bell Shaped
It is symmetric around the mean.
Mean, median, and the mode are plot at zero which is at the center of bell shape curve.
The curve does not touch the x-axis.
Differences between z and t distribution:
T- distribution is associated with degrees of freedom.
Degree of freedom is (n-1) and is associated with sample size.
Degree of freedom are the number of values that are free to vary after a sample statistics has been computed.
It tells the research which t curve to use.
With the increase in sample size, the t distribution approaches the standard normal distribution.
When to use t test:
Standard deviation of population is unknown. Use the s (standard deviation).
if sample size less than 30 so normal distribution should be ensured.
Steps for hypothesis testing for t test:
State null and alternative hypothesis.
Determine the level of significance
Apply test statistics.
Identify critical region/ p-value.
Interpret the result.
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- 2. Shakir Rahman BScN, MScN, MSc Applied Psychology, PhD Nursing (Candidate) Principal & Assistant Professor Ayub International College of Nursing & AHS Peshawar Visiting Faculty Swabi College of Nursing & Health Sciences Swabi Nowshera College of Nursing & Health Sciences Nowshera
- 3. By the end of the session, students will be able to: Apply the basics of inferential statistics in terms of point estimation. Compute point and estimation of population means and confidence interval. Interpret the results of point and interval estimation.
- 4. Descriptive Inferential Statistics Estimation Hypothesis testing Point Estimate Interval Estimate 3
- 5. A large group of your employees went to restaurant and ordered a dessert. None of you liked it. May be, 45% of them will prefer not eating it and leaving the restaurant and 15% of them will complaint about it to the waiter to get a fresh new dessert. With margin of error of 3% points. Youinterviewed 400 of employees.
- 6. How do mentioned estimations or predictionsare related to true population parameter? What is margin of error? Is the sample of 400 sufficient to claim anything about population of all employees ordering that dessert?
- 7. Estimating the value of parameter from thesample. An aspect of inferential statistics. Why to estimate: Population is large enough so we can only estimate. Types of estimation: Point Estimation: A specified number value (single value) that is an estimate of a population parameter.The point estimate of the population mean µ is the sample mean.
- 8. Interval Estimate: Range of values to estimate about population parameter. Example: What is an estimate of score of nursing students in entry test of Nursing school? (Out of 100 marks) a. 90 b. 80 c. 80-95 d. 75-85 Point Estimate Interval Estimate
- 9. The mean height of Pakistani girls at age 20 years is: a. 5.2 fts b. 5-5.5 fts c. 5 fts d. 5.1-5.6 fts Which of the following is an example of point estimate and which is an example of interval estimate.
- 10. • Sample statistics. • From random sampling • Aims to estimate about population parameter. - Ѕ ----- Estimates ----- ----- Estimates ----- µ • Repeated sampling in experiments will result in more than one sample means, among which any one could be a point estimator to estimate about population parameter or mean.
- 11. How good is the point estimate?
- 12. Confidence Interval Estimation. Range of values to estimate about population parameter. May contain the parameter or not (Degree of confidence). Ranges between two values. Example: Age (in years) 4 BScN students: 20<µ < 25 or (22.5 +2.5)
- 13. Population Parameter Upper Confidence Limit Lower ConfidenceLimit Width of Confidence Interval
- 14. Population Parameter (22.5 yrs) Upper Confidence Limit (25 yrs) Lower Confidence Limit (20 yrs) Width of Confidence Interval
- 15. FORMULA: _ Point estimate (x) + Critical Value x Standard Error
- 16. Confidence Interval is a particular interval ofestimate • Central Limit Theorem: •Given that sample size is large, the 95% of the sample means taken from same population and same sample size will fall in + 1.96 SD of the population mean. • _ _ • X + 1.96 σ/n
- 19. μ 16 Consider a 95% confidence interval: 1 .95 .05 / 2 .025 Z= 1.96 α .025 2 α .025 2 Upper Confidence Limit Point Estimation 0 .475 .475 Z= -1.96 Lower Confidence Limit μl Z μu
- 22. • Three commonly used Confidence Intervals are 90%, 95% (by default) , and 99%. • Why not too small or too large confidence intervals? Too wide: 99.9% Interval too broad Too narrow: 80 % More uncertainty to have population mean.
- 23. • The 99% of the sample means taken from same populationand same sample size will fall in + 2.575 SD of the population mean. _ _ X + 2.575 σ/n • Interpretation: 99% probability that interval will enclose population parameter and 1% chance that it will not have population parameter.
- 25. • Level of confidence (1- ) : The level ofcertainty that the interval will have the true population mean. • Chances of Error : Chances that the interval will not cater the true parameter. • Sum of level of confidence and chances of error =100%
- 26. The more the confidence, the wider will be the confidence interval.
- 28. FORMULA: _ Point estimate (x) + Critical Value x Standard Error
- 29. The survey of 30 emergency room patients found that the average waiting time for treatment was 174.3minutes. Given that the standard deviation is 46.5 minutes. Find the best point estimate of population parameter (mean). The confidence level is95%. Reference: Bluman (2012)
- 30. Point estimate (x) + Critical Value x StandardError 174.3 + 1.96 x 46.5/ √ 30 174.3 + 1.96 x 46.5/ 5.47 174.3 + 1.96 x 8.5 174.3 + 16.6 157.7, 190.9 (LL , UL) LL: Lower limit UL: Upper limit
- 31. Sample Size (Increase in sample sizewill narrow confidence interval). Increase in variability will increase confidence Interval.
- 33. Bluman (2012). Elementary Statistics: A Step by StepApproach (8th.). McGraw Hill. Daniel (2014). Biostatistics: Basic Concepts and Methodology for the Health Sciences. New York: John Wiley &Sons.
- 34. Acknowledgements Dr Tazeen Saeed Ali RM, RM, BScN, MSc ( Epidemiology & Biostatistics), Phd (Medical Sciences), Post Doctorate (Health Policy & Planning) Associate Dean School of Nursing & Midwifery The Aga Khan University Karachi. Kiran Ramzan Ali Lalani BScN, MSc Epidemiology & Biostatistics (Candidate) Registered Nurse (NICU) Aga Khan University Hospital