The agreement between your calculated test statistic and the predicted values is described by the p value. The more extreme your test statistic – the further to the edge of the range of predicted test values it is – the less likely it is that your data could have been generated under the null hypothesis of that statistical test. This shows the most likely range of values that will occur if your data follows the null hypothesis of the statistical test. The t value of the regression test is 2.36 – this is your test statistic.įor any combination of sample sizes and number of predictor variables, a statistical test will produce a predicted distribution for the test statistic. a t value comparing that coefficient to the predicted range of regression coefficients under the null hypothesis of no relationship.Test statistic exampleTo test your hypothesis about temperature and flowering dates, you perform a regression test. However, formulas to calculate these statistics by hand can be found online. In practice, you will almost always calculate your test statistic using a statistical program (R, SPSS, Excel, etc.), which will also calculate the p value of the test statistic. Null: The variation among two or more groups is greater than or equal to the variation between the groupsĪlternative: The variation among two or more groups is smaller than the variation between the groupsĪlternative: Two samples are not independent (i.e., they are correlated) Test statisticĪlternative: The means of two groups are not equalĪlternative:The means of two groups are not equal The t value compares the observed correlation between these variables to the null hypothesis of zero correlation.īelow is a summary of the most common test statistics, their hypotheses, and the types of statistical tests that use them.ĭifferent statistical tests will have slightly different ways of calculating these test statistics, but the underlying hypotheses and interpretations of the test statistic stay the same.

To test this hypothesis you perform a regression test, which generates a t value as its test statistic. Alternate hypothesis ( H A or H 1): There is a correlation between temperature and flowering date.Null hypothesis ( H 0): There is no correlation between temperature and flowering date.You use a long-term data set that tracks temperature and flowering dates from the past 25 years by randomly sampling 100 trees every year in an experimental field. Test statistic exampleYou are testing the relationship between temperature and flowering date for a certain type of apple tree. Generally, the test statistic is calculated as the pattern in your data (i.e., the correlation between variables or difference between groups) divided by the variance in the data (i.e., the standard deviation). The test statistic summarizes your observed data into a single number using the central tendency, variation, sample size, and number of predictor variables in your statistical model. Different statistical tests predict different types of distributions, so it’s important to choose the right statistical test for your hypothesis. The distribution of data is how often each observation occurs, and can be described by its central tendency and variation around that central tendency. Frequently asked questions about test statisticsĪ test statistic describes how closely the distribution of your data matches the distribution predicted under the null hypothesis of the statistical test you are using.

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