Statistical Tests and Interpretation

What test is used to examine the relationship between two categorical variables?

The chi-square test of independence.

What test is used to compare observed frequencies for one categorical variable with expected frequencies?

The chi-square goodness-of-fit test.

What does a chi-square test of independence evaluate?

Whether two categorical variables are statistically associated or independent.

What is the Pearson product-moment correlation (r) used for?

Measuring the direction and strength of a linear relationship between two continuous variables.

What assumptions are highlighted for Pearson correlation in this course guide?

The variables are measured at the interval or ratio level and have a linear relationship.

What values can Pearson's r take?

From −1 to +1.

What does a positive correlation mean?

As one variable increases, the other tends to increase.

What does a negative correlation mean?

As one variable increases, the other tends to decrease.

What does a correlation near zero mean?

There is little or no linear relationship; a nonlinear relationship may still exist.

Does correlation establish causation?

No. A correlation alone cannot show that one variable caused the other.

What is the difference between the correlational method and a correlation statistic?

The correlational method is a research approach without manipulation; a correlation statistic (such as r) is a numerical measure of association.

What data are used for chi-square tests?

Frequency counts for categorical (nominal) data.

Can a chi-square statistic be negative?

No. It is based on squared discrepancies between observed and expected frequencies.

What are the degrees of freedom for a chi-square test of independence?

df = (number of rows − 1) × (number of columns − 1).

What does a significant chi-square test of independence mean?

There is evidence of an association between the categorical variables; they are not statistically independent.

What should you examine after a significant chi-square test?

The cell percentages and standardized or adjusted residuals to see which categories contribute to the association.

What do chi-square residuals help identify?

Cells where observed counts differ more than expected under independence.

What is an independent-groups t test used for?

Comparing the means of a continuous DV between two unrelated groups.

When is an independent-groups t test appropriate?

There are two groups with different, unrelated participants and a continuous outcome.

Can an independent-groups t test establish causation?

Only when the groups were created through a suitable experiment with random assignment and other causal requirements met; naturally occurring groups do not establish causation.

What is the basic logic of an independent-groups t test?

Compare the two group means and evaluate whether their difference is larger than expected from sampling variation.

What are the degrees of freedom for the standard pooled independent t test?

df = n₁ + n₂ − 2 (total N − 2). Welch's t test uses a different df calculation.

What should be reported for an independent t test in a paper?

Group means (M), standard deviations (SD), the t statistic, degrees of freedom, p-value, and an effect size such as Cohen's d.

What is a paired-samples (correlated-groups) t test used for?

Comparing two related measurements, such as the same participants before and after a treatment or matched pairs.

What does a paired-samples t test analyze?

The difference score for each pair or participant.

What is the null hypothesis for a paired-samples t test?

The population mean difference score equals zero.

What are the degrees of freedom for a paired-samples t test?

df = N − 1, where N is the number of pairs or participants with both measurements.

What should be reported for a paired t test?

The means and SDs for the conditions, t statistic, df, p-value, and an appropriate effect size such as Cohen's d.

What is a one-way ANOVA used for?

Testing whether the means of a continuous DV differ across three or more levels of one categorical independent variable.

What is the null hypothesis for a one-way ANOVA?

All population group means are equal.

What is the alternative hypothesis for a one-way ANOVA?

At least one population mean differs from at least one other mean.

Why is the ANOVA alternative hypothesis nondirectional?

The omnibus test indicates whether any mean difference exists but does not specify which groups differ or the direction.

What is the F ratio in ANOVA?

A ratio comparing variability between groups to variability within groups.

What does a significant one-way ANOVA tell you?

At least one group mean differs, but it does not identify which specific groups differ.

What are post hoc tests used for?

After a significant independent-groups ANOVA, they identify which pairs of group means differ while controlling for multiple comparisons.

What effect sizes may be reported for ANOVA?

Eta-squared (η²) or omega-squared (ω²), depending on the analysis and course expectations.

What should be reported to describe ANOVA groups?

Group means (M) and standard deviations (SD), along with F, degrees of freedom, p-value, and an effect size.

What is an independent-groups one-way ANOVA?

A one-way ANOVA in which different participants are in each level of the IV.

What is a repeated-measures one-way ANOVA?

A one-way ANOVA in which the same participants provide scores in all levels of the IV.

What is a key advantage of repeated-measures ANOVA?

It controls for stable individual differences because the same participants are measured in every condition.

What is a key concern with repeated-measures ANOVA?

Order and carryover effects, as well as the repeated-measures assumptions such as sphericity when applicable.

What does a significant repeated-measures ANOVA indicate?

At least one condition mean differs from another; follow-up comparisons may be needed to identify where.

What is the general test-selection rule when both variables are categorical?

Use chi-square (independence for two variables; goodness-of-fit for one variable).

What is the general test-selection rule when both variables are continuous and you want their relationship?

Use Pearson correlation (if its assumptions are appropriate).

What is the general test-selection rule for a categorical IV and continuous DV with two unrelated groups?

Use an independent-groups t test.

What is the general test-selection rule for a categorical IV and continuous DV with two related measurements?

Use a paired-samples (correlated-groups) t test.

What is the general test-selection rule for a categorical IV with more than two unrelated groups and a continuous DV?

Use an independent-groups one-way ANOVA.

What is the general test-selection rule for more than two related conditions and a continuous DV?

Use a repeated-measures one-way ANOVA.

What is the difference between statistical significance and practical significance?

Statistical significance concerns how incompatible the data are with H₀; practical significance concerns whether the size of the effect matters in the real world.

How should a significant chi-square result be described?

State that the categorical variables were associated, then use percentages and residuals to describe the pattern.