The choices on this tab vary a bit depending on which test you chose on the first tab.

Calculations

The default choices for the calculation options will be fine for most people (two-tailed P values, 95% confidence intervals, and difference computed as the first column minus the second).

•One- or two-tailed P value. Choose a two-tailed P value, unless you have a strong reason not to.

•Report differences as. This determines the sign of the difference between means or medians that Prism reports. Do you want to subtract the second mean from the first, or the first from the second?

•Confidence level. 95% is standard, but you can pick another degree of confidence.

Graphing options

The options available in this section depend on which test you chose on the first tab. They can be useful to view the data with more depth, but none are essential to beginners, with the possible exception of the "Estimation Plot".

•Graph differences (paired) or Graph log(ratios). The paired t test and Wilcoxon matched pairs test first compute the difference between the two values on each row. This option creates a table and graph showing this list of differences. When performing a ratio paired t test, this option allows for the creation of a graph of the log of the ratios of the paired values (note that the log of a ratio of two values is mathematically equivalent to the difference of the logs of the two values).

•Graph ranks (nonparametric). The Mann-Whitney test first ranks all the values from low to high, and then compares the mean rank of the two groups. This option creates a table and graph showing those ranks. The Wilcoxon first computes the difference between each pair, and then ranks the absolute value of those differences, assigning negative values when the difference is negative.

•Graph correlation (paired). If a normal distribution is assumed, this graph plots the values of one group vs. the other to visually assess how correlated they are. If a lognormal distribution is assumed, the logarithm of the values for each group are plotted.

•Graph confidence interval of differences between means (Estimation Plot). This option generates a graph that includes a scatterplot (or violin) of the original data. Additionally, this graph includes a third dataset plotting the difference between means and 95% CI (for an unpaired test), or the mean of differences and a 95% CI (for a paired test). Estimation plots are very useful for visually assessing the results of t tests. Read more about how to understand and use Estimation plots. Note that if a lognormal distribution is assumed, these options are slightly different.

oFor an unpaired design with a lognormal distribution, an estimation plot is generated, graphing the logarithm of the values for each group along with the average of these logarithms (taking the exponential of this average provides the geometric mean for each group). A third group plotting the difference between the logarithm of each group average along with its 95% confidence interval is also provided. Taking the exponential of this value provides the ratio of geometric means between the two groups.

oFor a paired design with a lognormal distribution, this graph simply displays the geometric mean of the paired ratios along with its 95% confidence interval

Additional results

These options are not selected by default. The AIC option is for special purposes. The other options might be useful even to beginners.

•Descriptive statistics. Check this option, and Prism will create a new table of descriptive statistics for each data set.

•Also compare models using AICc.  Most people will not want to use this, as it is not standard. The unpaired t test essentially compares the fit of two models to the data  (one shared mean, vs. two separate group means). The t test calculations are equivalent to the extra sum-of-squares F test. When you check this option, Prism will report the usual t test results, but will also compare the fit of the two models by AICc, and report the percentage chance that each model is correct.

•Nonparametric tests. Compute the 95% CI for the difference between medians (Mann-Whitney) or the median of the paired differences (Wilcoxon). You can only interpret this confidence interval if you make an additional assumption not required to interpret the P value. For the Mann-Whitney test, you must assume that the two populations have the same shape (whatever it is). For the Wilcoxon test, you must assume that the distribution of differences is symmetrical. Statistical analyses are certainly more useful when reported with confidence intervals, so it is worth thinking about whether you are willing to accept those assumptions. Calculation details.

•Wilcoxon test. What happens when the two matching values in a row are identical? Prism 5 handled this as Wilcoxon said to when he created the test. Prism offers the option of using the Pratt method instead. If your data has lots of ties, it is worth reading about the two methods and deciding which to use.

•Report effect sizes (Cohen's d, Hedges' g, Glass's Δ). Check this option to calculate standardized effect sizes that quantify the magnitude of the difference between groups.

Effect sizes for t tests

When comparing two groups with t tests, P values tell you whether the difference is statistically significant, but they don't tell you how large or meaningful that difference is. Effect sizes provide standardized measures of the magnitude of differences between groups, making it easier to interpret the practical significance of your results and compare findings across different studies. Prism calculates several complementary effect size measures for t tests.

R squared (eta squared)

R squared (also called eta squared for t tests) represents the proportion of variance in the outcome variable that is explained by group membership. It ranges from 0 to 1, where 0 means group membership explains none of the variance and 1 means it explains all the variance. For example, an R squared of 0.14 means that knowing which group a value belongs to explains 14% of the variation in your data, while the remaining 86% is due to individual differences within groups. This measure is directly related to the t statistic and provides the same information as eta squared in ANOVA.

Cohen's d

Cohen's d expresses the difference between group means in terms of standard deviation units. It's calculated by dividing the difference between means by the pooled standard deviation. Cohen suggested these interpretation guidelines:

•Small effect: d ≈ 0.20

•Medium effect: d ≈ 0.50

•Large effect: d ≈ 0.80

A Cohen's d of 0.73, for example, means the two group means differ by 0.73 standard deviations. This is a moderately large effect, suggesting substantial practical significance beyond statistical significance.

Hedges' g

Hedges' g is a variation of Cohen's d that corrects for bias in small sample sizes. The correction is minimal with large samples but becomes more important when sample sizes are small (less than 20 per group). Hedges' g is generally preferred over Cohen's d for publication because it provides a more accurate estimate, especially in small samples. The interpretation guidelines are the same as for Cohen's d.

Glass's Δ (delta)

Glass's delta is similar to Cohen's d but uses only the control group's standard deviation as the denominator rather than pooling both groups. This is particularly useful when:

•The two groups have very different variability

•You're comparing an experimental group to a well-established control

•The treatment might affect variability as well as the mean

Glass's delta uses the same interpretation guidelines as Cohen's d.

Choosing and interpreting effect sizes

For most applications, we recommend reporting Hedges' g as it provides the most accurate estimate, particularly for small samples. However, all three standardized effect sizes (d, g, and Δ) tell similar stories about effect magnitude and are interpreted using the same guidelines.

Effect sizes are especially valuable when:

•You find a statistically significant difference but want to know if it's practically meaningful

•You're comparing results across different studies that used different measurement scales

•You're planning future studies and need to estimate the sample size needed to detect effects of a given magnitude

•You're conducting a meta-analysis combining results from multiple studies

Remember that even a large effect size doesn't necessarily mean a difference is important in your specific context, and a small effect size might still be scientifically or clinically meaningful. Always interpret effect sizes in light of your research question and field of study.