Hypothesis
Testing
Outline
 The Null Hypothesis
 Type I and Type II Error
 Using Statistics to test the Null Hypothesis
 The Logic of Data Analysis
Research Questions and Hypotheses
 Research question:
 Non-directional:
 No stated expectation about outcome
 Example:
 Do men and women differ in terms of conversational memory?
 Hypothesis:
 Statement of expected relationship
 Directionality of relationship
 Example:
 Women will have greater conversational memory than men
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 conversational
memory?
 Theoretical rationale based on:
 1. Past research
 2. Existing theory
 3. Logical reasoning
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 conversational memories
 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
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
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
Potential outcomes of testing
Decision
Accept Null
Reject Null
R
E
No
A
Relationship
1
2
3
4
L
I
T
Y
Relationship
Potential outcomes of testing
Decision
Accept Null
Reject Null
R
E
No
A
Relationship
Correct
decision
2
L
I
T
Y
Relationship
3
4
Potential outcomes of testing
Decision
Accept Null
Reject Null
R
E
No
A
Relationship
1
2
L
I
T
Y
Relationship
3
Correct
decision
Potential outcomes of testing
Decision
Accept Null
Reject Null
R
E
No
A
Relationship
1
Type I Error
L
I
T
Y
Relationship
3
4
Potential outcomes of testing
Decision
Accept Null
Reject Null
R
E
No
A
Relationship
1
2
L
I
T
Y
Relationship
Type II Error
4
Potential outcomes of testing
Decision
Accept Null
Reject Null
R
E
No
A
Relationship
Correct
decision
Type I Error
L
I
T
Y
Relationship
Type II Error
Correct
decision
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
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
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
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
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
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
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
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)
Variables
 Dependent variable:
 What we are trying to predict
 E.g., Candidate preference
 Independent variables:
 What we are using as predictors
 E.g., Gender, Party affiliation
Testing hypothesis for two
nominal variables
Variables
Null hypothesis
Procedure
Gender
Passing is not
related to gender
Pass/Fail
Chi-square
Testing hypothesis for one
nominal and one ratio variable
Variables
Null hypothesis
Procedure
Gender
Score is not
related to gender
Test score
T-test
Testing hypothesis for one
nominal and one ratio variable
Variable
Null hypothesis
Procedure
Year in school
Score is not
related to year in
ANOVA
school
Test score

Can be used when nominal variable has more than two categories and can
include more than one independent variable
Testing hypothesis for two ratio
variables
Variable
Null hypothesis
Procedure
Hours spent
studying
Score is not
related to hours
spent studying
Test score
Correlation
Testing hypothesis for more than
two ratio variables
Variable
Null hypothesis
Procedure
Hours spent
studying
Score is positively
related to hours
Classes
spent studying and
Multiple
missed
negatively related
regression
to classes missed
Test score
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
Summary of Statistical Procedures
Variables
Nominal IV, Nominal DV
Procedure
Chi-square
Nominal IV, Ratio DV
T-test
Multiple Nominal IVs, Ratio
DV
Ratio IV, Ratio DV
ANOVA
Multiple Nominal IVs, Ratio
DV with ratio covariates
ANCOVA
Multiple ratio
Multiple Regression
Pearson’s R