Statistical Analysis in Psychological Research

Manual: General · Subject: Psychology

Apply inferential statistics to test hypotheses, calculate effect sizes, and interpret psychological data.

12. Advanced Statistical Inference in Psychology

Inferential Statistics

Inferential statistics allow researchers to draw conclusions from sample data to a broader population. The independent samples t-test compares the means of two distinct groups. The formula calculates the ratio of the difference between group means to the variability of groups: $t = \frac{\bar{X}_1 - \bar{X}_2}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$ where $s_p$ is the pooled standard deviation.

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Statistical vs. Clinical Significance

A statistically significant result (e.g., $p < .05$ ) simply means the effect is unlikely due to chance. It does not necessarily mean the effect is large or practically meaningful (clinical significance).

Analysis of Variance (ANOVA) Variants

One-Way ANOVA

Tests for differences among three or more independent groups on a single continuous variable.

Factorial ANOVA

Examines the main effects and interaction effects of two or more independent variables.

Repeated Measures ANOVA

Used when the same subjects are measured multiple times under different conditions.

In Null Hypothesis Significance Testing (NHST), what constitutes a Type I error?

Failing to reject a false null hypothesis Rejecting a true null hypothesis Accepting a true alternative hypothesis Rejecting a false alternative hypothesis

Effect Size

Because p-values are heavily influenced by sample size, modern psychology emphasizes reporting effect sizes. Cohen's $d$ quantifies the standardized difference between two means: $d = \frac{M_1 - M_2}{SD_{pooled}}$ A $d$ of 0.2 is considered small, 0.5 medium, and 0.8 large.

Null Hypothesis Significance Testing (NHST)

1

State the Null Hypothesis ( $H_0$ ) and Alternative Hypothesis ( $H_1$ ).
2

Set the alpha level (typically $\alpha = .05$ ).
3

Calculate the test statistic (e.g., t, F, $\chi^2$ ).
4

Determine the p-value associated with the test statistic.
5

Compare the p-value to alpha to make a decision regarding $H_0$ .

What is the term for the probability of finding the observed, or more extreme, results when the null hypothesis is true?

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Statistical Analysis in Psychological Research

12. Advanced Statistical Inference in Psychology

Inferential Statistics

Effect Size

Null Hypothesis Significance Testing (NHST)