ANOVA and Chi-Square Tests Review

Repeated Measures ANOVAs

Definition: A repeated measures ANOVA, also known as a within-subjects ANOVA, is a statistical technique used when multiple measurements are taken from the same subjects, allowing researchers to assess whether there are statistically significant differences among the group means. This method controls for inter-subject variability, leading to greater statistical power.

SPSS Procedures:

• Navigate to Analyze → General Linear Model → Repeated Measures.

Define Repeated Measures:

1. Within Factor Name: Enter the name for the within-subject factor.

2. Levels of Independent Variable (IV): Specify the different levels for the IV (e.g., Pre-test, Post-test).

3. Match the factor labels with the levels specified for clarity during analysis.

Options:

• Turn on descriptive statistics to compute mean values and standard deviations for each level for a better understanding of data distribution.

Plots:

• For visualization, select the Horizontal Axis and choose a line chart. This provides a clear graphic representation of mean trends across different measurements.

F-test Reporting in APA Style:

• When reporting results, format as: F(df{iv}, df{Error}) = _., p. Here, df{iv} represents the degrees of freedom of the independent variable, and df{Error} represents the degrees of freedom for error, both of which rely on assumptions of sphericity.

• If results are not significant, report findings as n.s. (not significant).

• Example Report: F(3, 18) = 8.14, p < .05 indicates a statistically significant difference among group means.

Two-Way ANOVAs

Definition: A two-way ANOVA is utilized to examine the interaction effects between two independent variables (factors) on a dependent variable, allowing researchers to understand how different conditions may influence outcomes in conjunction.

SPSS Procedures:

• Navigate to Analyze → General Linear Model → Univariate.

Independent Variables (IVs):

• Input each independent variable into the fixed factors section. This might include treatments or conditions being tested.

Options:

• Enable Descriptive Statistics to provide additional insights into the data such as means and standard deviations.

Plots:

• Assign each independent factor to either the Horizontal Axis or create separate lines for clarity. A line chart allows easy visual interpretation of potential interactions.

Important Considerations:

• Estimated Marginal Means (EM) should not be solely relied upon as they provide standard errors rather than standard deviations, which may misrepresent data variability.

Reporting Main Effects:

• Clearly present means and standard deviations. Example: (M = 2.83, SD = 3.58)

Reporting Interactions:

• For significant tests of interaction, detail: Exercise x Relationship degrees of freedom, F-statistic, and significance levels. An example might state: "The interaction was not significant (F(1, 20) = 0.06, n.s.)."

Chi-Square Tests of Independence

Definition: A chi-square test is a statistical method used to determine whether there is a significant association between categorical variables by comparing the observed frequencies in a contingency table to the frequencies expected under the null hypothesis.

SPSS Procedures:

• Navigate to Analyze → Descriptive Statistics → Crosstabs.

• Within the crosstabs menu:

  • Select Cells to include Expected Values for comparison.

  • Under Statistics, choose Chi-square for the relevant calculations.

Interpretation Guidelines:

• In the Contingency Table: Columns typically represent the different levels of one variable (e.g., treatment type), while Rows represent the corresponding levels of another variable (e.g., response type).

• To display expected values in the crosstabs output, ensure the corresponding option is selected in the Crosstabs dialog to facilitate accurate interpretation of results.

Chi-square Reporting in APA Style:

• Format should be: 𝜒²(df, N = ) = _., sig., where N denotes the total number of observations involved in the analysis.

• Degrees of freedom can be found under the df section of the results.

• Example Report: 𝜒²(4, N = 344) = 4.08, n.s. indicates a non-significant association.

Helpful Tips:

• When analyzing a repeated measures ANOVA, focus primarily on within-subject effects to determine significant differences based on your independent variable over time or conditions.

• It's essential to remember that in statistical reporting, only letters (e.g., 𝜒², F) should be italicized to adhere to APA style specifics.