# Two-independent sample t-test

**BRIEF DESCRIPTION**

The Two-independent sample t-test is for continuous scaled data and it compares the observed mean on the dependent variable between two groups as defined by the independent variable. For example, is the mean customer satisfaction score (on the dependent variable) significantly different between men and women (on the independent variable). The t-test is a parametric procedure.

**SIMILAR STATISTICAL PROCEDURES**

**Non-parametric counterparts**of the Two-independent t-test include the (Wilcoxon) Mann-Whitney U-test (non-parametric), Wald-Wolfowitz Runs test, Kolmogorov-Smirnov Z test, Moses Extreme Reactions test, Chi-Square (χ²) test of independence, and Fisher’s Exact test**One-sample t-test**(compares an observed sample mean of a single variable with a predetermined value such as a benchmark mean)**Paired t-test**(parametric) allows for matched (dependent groups) to be compared over time. Non-parametric counterparts include the Wilcoxon matched pairs test, Sign test, McNemar test, and the Marginal Homogeneity test.

**CHARACTERISTICS OF THE VARIABLES**

**Dependent variable**: continuous scaled data**Independent variable**: categorical data with two groups

**DATA ASSUMPTIONS**

- Continuous scaled data.
- Population is normally distributed although it suffices if the sample data does not significantly deviate from a normal distribution.
- Independence of observations and groups.
- Random sampling from a defined population.
- No outliers.
- Homogeneity of variance: Variance of the two different groups are roughly equal (measured by the Levene’s test). If the Levene’s test is significant at e.g. p‘<‘0.05 then we reject the null hypothesis so we conclude that variances differ significantly between the two groups so the assumption has been violated. Note that t-tests are relatively robust to violations of this assumption if group sizes are fairly equal. However, if violated, report the results for “equal variances not assumed”.

**WHERE TO FIND IN SPSS?**

ANALYZE / COMPARE MEANS/ INDEP-SAMPLE T-TEST

**HOW TO REPORT THE FINDINGS?**

If the t-test is significant (e.g. p‘<‘.05) we reject the null hypothesis so it indicates that the mean scores between the two groups differ significantly from each other (significant effects).

**Reporting example**: “A Two-independent groups t-test was performed examining difference between males and females on their customer satisfaction scores. A significant difference was found between males and females, t (15) = 2.50, p‘<‘. 05. Examination of the means showed that females (mean = 3.1, sd = 1.0) have a higher satisfaction than males (mean = 1.8, sd = 0.5)”. The actual p-value can be reported in lieu of the ‘<‘.05 (e.g. p=.041). At the end you may want to indicate the effect size (Cohen’s d) e.g. d=.45. Cohen’s d measures difference of means in standard deviation units. NOTE: If p‘>‘.05 you don’t report the value (e.g. p‘>‘.05 or p=.129) but only indicate it as NS (non-significant).**Explanation of the above example**: The t refers to our Two-independent sample t-test procedure, the 15 in brackets is the degrees of freedom (df), the 2.50 is the actual t-test value, and the p‘<‘.05 indicates an actual p-value which is less (e.g. .023) than our chosen confidence level of .05.

**FURTHER COMMENTS.**

Be careful with any significance tests if you have a large sample, at which time it becomes critical to calculate the effect size (Cohen’s d).

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