P Value Between Two Groups Calculator

[Enrichetta]

This procedure calculates the difference between the observed means in two independent samples. A significance value (P-value) and 95% Confidence Interval (CI) of the difference is reported. The P-value is the probability of obtaining the observed difference between the samples if the null hypothesis were true. The null hypothesis is the hypothesis that the difference is 0.

A t test is used to measure the difference between exactly two means. Its focus is on the same numeric data variable rather than counts or correlations between multiple variables. If you are taking the average of a sample of measurements, t tests are the most commonly used method to evaluate that data. It is particularly useful for small samples of less than 30 observations. For example, you might compare whether systolic blood pressure differs between a control and treated group, between men and women, or any other two groups.

This calculator uses a two-sample t test, which compares two datasets to see if their means are statistically different. That is different from a one sample t test, which compares the mean of your sample to some proposed theoretical value.

Correlation and regression are used to measure how much two factors move together. While t tests are part of regression analysis, they are focused on only one factor by comparing means in different samples.

Finally, contingency tables compare counts of observations within groups rather than a calculated average. Since t tests compare means of continuous variable between groups, contingency tables use methods such as chi square instead of t tests.

Because there are several versions of t tests, it's important to check the assumptions to figure out which is best suited for your project. Here are our analysis checklists for unpaired t tests and paired t tests, which are the two most common. These (and the ultimate guide to t tests) go into detail on the basic assumptions underlying any t test:

The three different options for t tests have slightly different interpretations, but they all hinge on hypothesis testing and P values. You need to select a significance threshold for your P value (often 0.05) before doing the test.

While P values can be easy to misinterpret, they are the most commonly used method to evaluate whether there is evidence of a difference between the sample of data collected and the null hypothesis. Once you have run the correct t test, look at the resulting P value. If the test result is less than your threshold, you have enough evidence to conclude that the data are significantly different.

If the test result is larger or equal to your threshold, you cannot conclude that there is a difference. However, you cannot conclude that there was definitively no difference either. It's possible that a dataset with more observations would have resulted in a different conclusion.

Depending on the test you run, you may see other statistics that were used to calculate the P value, including the mean difference, t statistic, degrees of freedom, and standard error. The confidence interval and a review of your dataset is given as well on the results page.

This calculator does not provide a chart or graph of t tests, however, graphing is an important part of analysis because it can help explain the results of the t test and highlight any potential outliers. See our Prism guide for some graphing tips for both unpaired and paired t tests.

Prism is built for customized, publication quality graphics and charts. For t tests we recommend simply plotting the datapoints themselves and the mean, or an estimation plot. Another popular approach is to use a violin plot, like those available in Prism.

When designing a trial to assess the effectiveness of a new therapy treatment on the treatment of severe sepsis and septic shock, how many patients are required in the treatment (new therapy) and control (standard therapy) groups? The clinicians measure the effectiveness of the therapies of the treatments using mean arterial pressures and wish to detect a difference of at least 14mmHg between the two groups (the standard deviation of the two groups is 20mmHg, i.e., the variance is 400mmHg). In order to detect a difference of this magnitude that is significant with 95% confidence and a power of 80%, the clinicians will require 33 patients in each group.

Note: This is a standard formula based on the normal distribution. References can be found in many texts, for example the Estimation of Sample Size and Power for Comparing Two Means section in Rosner, B., (2015). Fundamentals of Biostatistics. 8th ed. USA: Cengage Learning.

Statistical significance specifies, if a result may not be the cause of random variations within the data. But not every significant result refers to an effect with a high impact, resp. it may even describe a phenomenon that is not really perceivable in everyday life. Statistical significance mainly depends on the sample size, the quality of the data and the power of the statistical procedures. If large data sets are at hand, as it is often the case f. e. in epidemiological studies or in large scale assessments, very small effects may reach statistical significance. In order to describe, if effects have a relevant magnitude, effect sizes are used to describe the strength of a phenomenon. The most popular effect size measure surely is Cohen's d (Cohen, 1988), but there are many more.

Here you will find a number of online calculators for the computation of different effect sizes and an interpretation table at the bottom of this page. Please click on the grey bars to show the calculators:

If the two groups have the same n, then the effect size is simply calculated by subtracting the means and dividing the result by the pooled standard deviation. The resulting effect size is called dCohen and it represents the difference between the groups in terms of their common standard deviation. It is used f. e. for comparing two experimental groups. In case, you want to do a pre-post comparison in single groups, calculator 4 or 5 should be more suitable, since they take the dependency in the data into account.

If there are relevant differences in the standard deviations, Glass suggests not to use the pooled standard deviation but the standard deviation of the control group. He argues that the standard deviation of the control group should not be influenced, at least in case of non-treatment control groups. This effect size measure is called Glass' Δ ("Glass' Delta"). Please type the data of the control group in column 2 for the correct calculation of Glass' Δ.

Finally, the Common Language Effect Size (CLES; McGraw & Wong, 1992) is a non-parametric effect size, specifying the probability that one case randomly drawn from the one sample has a higher value than a randomly drawn case from the other sample. In the calculator, we take the higher group mean as the point of reference, but you can use (1 - CLES) to reverse the view.

Analogously, the effect size can be computed for groups with different sample size, by adjusting the calculation of the pooled standard deviation with weights for the sample sizes. This approach is overall identical with dCohen with a correction of a positive bias in the pooled standard deviation. In the literature, usually this computation is called Cohen's d as well. Please have a look at the remarks bellow the table.

The Common Language Effect Size (CLES; McGraw & Wong, 1992) is a non-parametric effect size, specifying the probability that one case randomly drawn from the one sample has a higher value than a randomly drawn case from the other sample. In the calculator, we take the higher group mean as the point of reference, but you can use (1 - CLES) to reverse the view.

Intervention studies usually compare the development of at least two groups (in general an experimental group and a control group). In many cases, the pretest means and standard deviations of both groups do not match and there are a number of possibilities to deal with that problem. Klauer (2001) proposes to compute g for both groups and to subtract them afterwards. This way, different sample sizes and pre-test values are automatically corrected. The calculation is therefore equal to computing the effect sizes of both groups via form 2 and afterwards to subtract both. Morris (2008) presents different effect sizes for repeated measures designs and does a simulation study. He argues to use the pooled pretest standard deviation for weighting the differences of the pre-post-means (so called dppc2 according to Carlson & Smith, 1999). That way, the intervention does not influence the standard deviation. Additionally, there are weighting to correct for the estimation of the population effect size. Usually, Klauer (2001) and Morris (2002) yield similar results.

The downside to this approach: The pre-post-tests are not treated as repeated measures but as independent data. For dependent tests, you can use calculator 4 or 5 or 13. transform eta square from repeated measures in order to account for dependences between measurement points.

While steps 1 to 3 target at comparing independent groups, especially in intervention research, the results are usually based on intra-individual changes in test scores. Morris & DeShon (2002, p.109) suggest a procedure to estimate the effect size for single-group pretest-posttest designs by taking the correlation between the pre- and post-test into account:

In case, the correlation is .5, the resulting effect size equals 1. Comparison of groups with equal size (Cohen's d and Glass Δ). Higher values lead to an increase in the effect size. Morris & DeShon (2008) suggest to use the standard deviation of the pre-test, as this value is not influenced by the intervention, thus resembling Glass Δ. It is referred to as dRepeated Measures (dRM) in the following. The second effect size dRepeated Measures, pooled (dRM, pool) is using the pooled standard deviation, controlling for the intercorrelation of both groups (see Lakens, 2013, formula 8). Finally, another pragmatic approach, often used in meta analyses, is to simply divide the mean difference between both measurements by the averaged standard deviation without controlling for the intercorrelation - an effect size termed dav by Cummings (2012).

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