3. “Education at home is a friend,
abroad an introduction, in solitude
a solace, and in society an
ornament. It gives once grace
and government to genius”
---Bharthruhari
4. The term statistical
significance is coined by
Ronald Fisher(18901962)
Student (William Sealy
Gosset) (1876-1937)
Carl Friedrich Gauss
(1777-1855)
5.
Range of estimates a characteristic can take (different samples are taken
from same population) depends on
1.the mean value
2.the variability of the observations in the original population
3.the size of the sample
Causes of differences observed between two estimates are
a) sample variation
b) when sample is coming from different population
Repeated samples even though from the same population will not yield
the same characteristic under observation(esp common among
biological observation). This difference between the sample estimates is
known as sample variation
6.
The methodologies of statistics which deal with the
technique to analyse, how far the difference between the
estimates from different samples are due to sampling
variation otherwise, is known as testing of hypothesis or
Statistical test is a procedure to find the likelihood of a null
hypothesis being right on the basis of the given data
Tests of significance is a procedure to test whether or not
the observations fall into a specified pattern such as
equality of two means or of two proportions
.
In statistics, a result is called statistically significant if it is
unlikely to have occurred by chance
7. Should be framed in such a way that it
conveys the meaning that differences
between the estimates provided by different
sample is due to the sampling variance
In other word, the null hypothesis states that
the samples are coming out of a common
population
8.
The amount of evidence required to accept that an event unlikely to have risen by
chance is known as the significance level or critical P-value(probability level)
It fixes the magnitude of risk of making a wrong conclusion of rejecting the null
hypothesis
If the value of P is small, it means that the probability of attributing the
difference between sample estimates to the sampling variation or chance factor
is small--- null hypothesis is rejected
If P value is large then the probability that the difference between the sample
estimates caused by sampling variation is large
How small should be this value of P to a reject a null hypothesis depends upon
the type of investigation. As a mater of practical convenience a value of less than
or equal to0.05 is the usual level which is commonly accepted for rejecting the
null hypothesis( it means one would be going wrong in 5 out of 100 cases by
rejecting the null hypothesis)
All tests of significance are aimed at finding this value of P
9. Errors in accepting or rejecting the null
hypothesisare
Type1 error – if the null hypothesis is rejected
when it is actually true
Type 2 error– if the null hypothesis is
accepted when it is false
10. It is the standard deviation of a statistical parameter
like mean, proportion, etc. this gives an idea about
satatistical parameters obtained from repeated
samples from the same population
Standard error is useful for fixing the confidence limits,
which gives a range for the statistical parameter,
indicating that the true value of the parameter is
contained in the range with a certain confidence
It is basic statistical quantity for testing the significance
of the difference in estimates between two samples
11.
12. Two tailed tests– in testing hypothesis
conclusion are made on the basis of tests of
significance that the two samples are from
the same population or not without
considering the direction of the difference
between the two sample estimates like mean
or proportion
One tailed tests– conclusions are made as to
whether one of the sample mean is larger
than the other, tests of significance
13. “Among all types of charities such as
of good food, water, cows, lands,
clothes, gold etc; a charity, donation
or grant forth spread of education is
superior to all other forms of
charities”
----Manu
14.
Based on specific
distribution such as
Gaussian
Not based on any
particular parameter such
as mean
Donot require that the
means follow a particular
distribution such as
Gaussian(have less
efficiency when underlying
distribution is Gaussian
Used when the underlying
distribution is far from
Gaussian (applicable to
almost all levels of
distribution) and when the
sample size is small
15. Student’s t- test(one
sample, two sample,
and paired)
Proportion
test(Gaussian’s z-test)
ANOVA F-test
Sign test(for paired
data)
Wilcoxon signed rank
test for matched pair
Wilcoxon rank sum test
(for unpaired data)
Chi-square test
Many tests based on
qualitative data are
nonparametric
16.
Students t- tests--A statistical criterion to test the
hypothesis that mean is superficial value, or that specified
difference, or no difference exists between two means. It
requires Gaussian distribution of the values, but is used
when SD is not known
Proportion test---A statistical test of hypothesis based on
Gaussian distribution, generelly used to compare two
means or two proportions in large samples, particularly
when the SD is known
ANOVA F-test--- used when the number of groups
compared are three or more and when the objective is to
compare the means of a quantative variable
17. One sample– only one group is studied and
an externally determined claim is examined
Two sample– there are two groups to
compare
Paired– used when two sets of
measurements are available, but they are
paired
18. Get up, be awake, resort to the
good and acquire knowledge
--- vedas
19.
Find the difference between the actually observed
mean and the claimed mean.
Estimate the standard error (SE) of mean by S/n,
where s is the standard deviation and n is the
number of subjects in the actually studied sample.
The SE measures the inter-sample variability
Check the the difference obtained in step 1 is
sufficiently large relative to the SE. for this ,
calculate students t. this is called the test criterion.
Rejection or non-rejection of the null depends on
the value of this t (this is similar to z-score of mean,
but not exactly the same)
Reject the null hypothesis if the t-value so
calculated ismore than the critical value
corresponding to the pre-fixed alpha level of
significance and appropriate df.
22. Obtain the difference for each pair and test
the null hypothesis that the mean of these
diffrences is zero(this null hypothesis is same
as saying that the means before and after are
equal)
24.
Situations where it is used
are
1.in a two sample situation
2. in a paired set-up
3.in a repeated measures,
when the same subject is
measured at different time
points such as after 5
minutes, 15 minutes, 30
minutes, 60 minutes etc,.
4.removing the effect of a
covariate
5. regression.
25. Based on signs(positive and negative) of the
differences in the levels seen before and after
therapy
26. It is better test than the sign test– assigns
rank to the differences of n pairs after
ignoring the + or – signs
The lowest difference gets rank 1 and the
highest gets rank n
Sum of the only those ranks that are
associated with positive difference
obtained(Wilcoxon signed rank criteria)
It is similar to Mann-Whitney test
27. If there are n1 subjects in the first sample
andn2inthe second sample, these(n1+n2)
values are jointly ranked from 1 to (n1+n2)
{the sum of these ranks is obtained for those
subjects only who are in smaller group}
28. Alternative to the test of significance of
difference between two proportions
29. “Never shed tears for errors. Take
lessons from them you will win”
___Panchatantra
30. A Indrayan and L Satyanarayana-
biostatistics, 20006 ed, Printice -Hall of India
MSN Rao, NS Murthy-applied statistics in
health sciences, 2nd ed, 2010, jaypee
www. Wikipedia. org
