2. Outline
• The Null Hypothesis
• Type I and Type II Error
• Using Statistics to test the Null Hypothesis
• The Logic of Data Analysis
3. Research Questions and Hypotheses
• Research question:
– Non-directional:
• No stated expectation about outcome
– Example:
• Do men and women differ in terms of brand loyalty?
• Hypothesis:
– Statement of expected relationship
• Directionality of relationship
– Example:
• Women will have greater brand loyalty than men
4. Grounding Hypotheses in Theory
• Hypotheses have an underlying rationale:
– Logical reasoning behind the direction of the
hypotheses (theoretical rationale – explanation)
– Why do we expect women to have better brand
loyalty?
• Theoretical rationale based on:
– 1. Past research
– 2. Existing theory
– 3. Logical reasoning
5. The Null Hypothesis
• Null Hypothesis - the absence of a relationship
– E..g., There is no difference between men’s and
women’s with regards to brand loyalty
• Compare observed results to Null Hypothesis
– How different are the results from the null hypothesis?
• We do not propose a null hypothesis as research
hypothesis - need very large sample size / power
– Used as point of contrast for testing
6. Hypotheses testing
• When we test observed results against null:
– We can make two decisions:
• 1. Accept the null
– No significant relationship
– Observed results similar to the Null Hypothesis
• 2. Reject the null
– Significant relationship
– Observed results different from the Null Hypothesis
– Whichever decision, we risk making an error
7. Type I and Type II Error
• 1. Type I Error
– Reality: No relationship
– Decision: Reject the null
• Believe your research hypothesis have received support when in fact
you should have disconfirmed it
• Analogy: Find an innocent man guilty of a crime
• 2. Type II Error
– Reality: Relationship
– Decision: Accept the null
• Believe your research hypothesis has not received support when in
fact you should have rejected the null.
• Analogy: Find a guilty man innocent of a crime
8. Potential outcomes of testing
Decision
Accept Null Reject Null
R
E No
1 2
A Relationship
L
I Relationship
T
3 4
Y
9. Potential outcomes of testing
Decision
Accept Null Reject Null
Correct
R
E No
decision 2
A Relationship
L
I Relationship
T
3 4
Y
10. Potential outcomes of testing
Decision
Accept Null Reject Null
R
E
A
No
Relationship
1 2
L
I Relationship
T
Y
Correct
3 decision
11. Potential outcomes of testing
Decision
Accept Null Reject Null
R
E No 1 Type I Error
A Relationship
L
I Relationship
T
Y
3 4
12. Potential outcomes of testing
Decision
Accept Null Reject Null
R
E No 1 2
A Relationship
L
I Relationship
T
Y
Type II Error
4
13. Potential outcomes of testing
Decision
Accept Null Reject Null
Correct
Type I Error
decision
R
E No
A Relationship
L
I Relationship
T
Y Correct
Type II Error
decision
14. Function of Statistical Tests
• Statistical tests determine:
– Accept or Reject the Null Hypothesis
• Based on probability of making a Type I
error
– Observed results compared to the results
expected by the Null Hypotheses
– What is the probability of getting observed
results if Null Hypothesis were true?
• If results would occur less than 5% of the time by
simple chance then we reject the Null Hypothesis
15. Start by setting level of risk of
making a Type I Error
• How dangerous is it to make a Type I Error:
– What risk is acceptable?:
• 5%?
• 1%?
• .1%?
– Smaller percentages are more conservative in
guarding against a Type I Error
• Level of acceptable risk is called “Significance level” :
– Usually the cutoff - <.05
16. Conventional Significance Levels
• .05 level (5% chance of Type I Error)
• .01 level (1% chance of Type I Error)
• .001 level (.1% chance of Type I Error)
• Rejecting the Null at the .05 level means:
– Taking a 5% risk of making a Type I Error
17. Steps in Hypothesis Testing
• 1. State research hypothesis
• 2. State null hypothesis
• 3.Set significance level (e.g., .05 level)
• 4. Observe results
• 5. Statistics calculate probability of results if
null hypothesis were true
• 6. If probability of observed results is less than
significance level, then reject the null
18. Guarding against Type I Error
• Significance level regulates Type I Error
• Conservative standards reduce Type I Error:
– .01 instead of .05, especially with large sample
• Reducing the probability of Type I Error:
– Increases the probability of Type II Error
• Sample size regulates Type II Error
– The larger the sample, the lower the
probability of Type II Error occurring in
conservative testing
19. Statistical Power
• The power to detect significant relationships
– The larger the sample size, the more power
– The larger the sample size, the lower the
probability of Type II Error
• Power = 1 – probability of Type II Error
20. Statistical Analysis
• Statistical analysis:
– Examines observed data
– Calculates the probability that the results could
occur by chance (I.e., if Null was true)
• Choice of statistical test depends on:
– Level of measurement of the variables in
question:
• Nominal, Ordinal, Interval or Ratio
21. Logic of data analysis
• Univariate analysis
– One variable at a time (descriptive)
• Bivariate analysis
– Two variables at a time (testing relationships)
• Multivariate analysis
– More than two variables at a time (testing
relationships and controlling for other variables)
22. Variables
• Dependent variable:
– What we are trying to predict
– E.g., Brand preference
• Independent variables:
– What we are using as predictors
– E.g., Gender, Product usage history
23. Commonality across all statistical
analysis procedures
• Set the significance level:
– E.g., .05 level
• Means that we are willing to conclude that there is a
relationship if:
– Chance of Type I error is less than 5%
• Statistical tests tell us whether:
– The observed relationship has less than a 5%
chance of occurring by chance
24. Summary of Statistical Procedures
Variables Procedure
Nominal IV, Nominal DV Chi-square
Nominal IV, Ratio DV T-test
Multiple Nominal IVs, Ratio ANOVA
DV
Ratio IV, Ratio DV Pearson’s R
Multiple Nominal IVs, Ratio ANCOVA
DV with ratio covariates
Multiple ratio Multiple Regression
