Exam
enla
comm3023_ch12p3_2020.pptx
Chapter 12
Quantitative Data Analysis: Part 3
Testing Hypotheses of Differences
Hypotheses of differences focus on predicting differences in the dependent variable across different levels of an independent variable.
There are 3 options available for testing differences across groups:
Chi-square
t-test
Analysis of variance (ANOVA)
Chi-Square
Examines whether frequencies found for different levels of the dependent variable is influenced by different levels of the independent variable.
Chi-square looks at comparing observed frequencies to expected frequencies.
Chi-square statistic can be calculated by using cross-tabulations or contingency tables.
Rows represent the dependent variable
Columns represent the independent variable
Attitude Toward Gun Control by Sex: Frequency Table
Measures of Association For Nominal or Ordinal-Level Variables
To determine how strongly frequencies are related between 2 nominal or ordinal-level variables, a variety of measures can be used:
Percentage differences
Cramer’s phi coefficient
Chi-square statistic
The chi-square statistic requires that both the IV and the DV are at the nominal or ordinal-level of measurement.
t-test
Examines whether mean differences in the dependent variable across 2 groups is influenced by the independent variable.
Compares observed mean differences between 2 groups to expected mean differences based on chance.
The t-test is used only when the following are met:
The IV is a nominal-level variable with 2 categories or levels
The DV is an interval or ratio-level variable
t-test
There are 4 types of t-tests available depending on 2 factors
Independent vs. paired samples
One-tailed vs. two-tailed test
Analysis of Variance (ANOVA)
An ANOVA allows us to determine whether mean differences in the dependent variable across 3 or more groups is influenced by the independent variable.
Types of ANOVAs used depend on specific conditions:
One-way ANOVA
Factorial ANOVA
MANOVA
Additional variations of the ANOVA:
ANCOVA
Repeated-measures ANOVA
Analysis of Variance (ANOVA)
The F statistic (or F-ratio) is calculated to determine whether 3 or more group means significantly differ from each other in terms of the dependent variable.
The F-ratio compares the average variance between the groups examined to the average variance within each group.
Average variance between groups is known as mean square between (MSB).
Average variance within each group is known as mean square within (MSW).
Determining Significance in Hypothesis Testing
When testing hypotheses of covariation or hypotheses of differences, significance is determined by comparing the calculated inferential statistic to the critical inferential statistic value found in a table.
The chi-square, t-statistic, and F-statistic each have their own tables of critical values based on a normal distribution of data.
A hypothesis is supported if the calculated statistic is greater than the critical value.
A hypothesis is not supported if the calculated statistic is lesser than or equal to the critical value.
