t-test

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Contents 1 History 2 Types 2.1 One-sample t-test 2.2 Independent samples t-test 2.3 Paired samples t-test 3 Assumptions 4 Graphing 5 Write-up 5.1 Checklist 5.2 Example 1 6 See also 6.1 Non-parametric

[edit] History

The 100th birthday of the t-test was celebrated in 2008! The t statistic was introduced by William Sealy Gosset for cheaply monitoring the quality of beer brews ("Student" was his pen name). Gosset was a statistician for the Guinness brewery in Dublin, Ireland, and was hired due to Claude Guinness's innovative policy of recruiting the best graduates from Oxford and Cambridge to apply biochemistry and statistics to Guinness' industrial processes. Gosset published the t test in Biometrika in 1908, but was forced to use a pen name by his employer who regarded the fact that they were using statistics as a trade secret. Read more about its fascinating history here: t-test history.

[edit] Types

There are three types of t-test:

[edit] One-sample t-test

1. Used to compare a sample mean with a known population mean or some other meaningful, fixed value

[edit] Independent samples t-test

1. Used to compare two means from independent groups

[edit] Paired samples t-test

1. Used to compare two means that are repeated measures for the same participants - scores might be repeated across different measures or across time.

[edit] Assumptions

Dependent variables must be:

1. Measured at interval or ratio level level of measurement - i.e., needs to be continuous.
2. Normally distributed in all groups of the independent variable.
   • Robust to violations of this assumption if sample sizes are large and approximately equal (> 15 cases per group)
3. Have approximately equal variance across all groups of the IV (homogeneity of variance e.g., tested by Levene's test).
   • If not the p-values for significance tests are inaccurate.
   • If the variances are different SPSS has post-hoc tests to adjust for this.
4. Cases represent random samples from the populations and the scores of the test variable are independent of each other.
   • Inaccurate p-values if the independence assumption is violated.

[edit] Graphing

1. Bar chart (1 IV) and clustered bar charts (> 1 IV)
2. Box and whisker plot
3. Error-bar chart
4. Stem and leaf plot

[edit] Write-up

[edit] Checklist

1. Purpose
2. Variables / design
3. Descriptive statistics (4 moments)
4. Assumptions
5. Figure / graph? (optional)
6. Test statistics, including effect size and direction of effects

[edit] Example 1

An independent t-test was used to determine whether there was a difference in mean grip strength between males and females. This revealed a significant difference (t (88) = 2.04, p = .04), with males having significantly higher mean strength scores than females (males, M = 2.93, SD = 1.23; females, M = 2.71, SD = '1.41).

Note: Usually means, standard deviations and effect sizes are reported in a Table.

[edit] See also

• ANOVA
• Testing differences
• Welch's t test
• z-test

[edit] Non-parametric

• Mann-Whitney U
• Wilcoxon signed-rank test