Researchers and scientists often use statistical tests called t-tests to assess whether two groups of data differ from each another. A t-test compares the means of each group and takes into account the numbers on which the means are based to determine the amount of data overlap between the two groups. The test also tells you how significant the differences are between the two groups and reveals whether those differences could have happened by chance or are statistically significant.
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In statistics, t-tests are used to compare the means of two groups. Although a negative t-value shows a reversal in the directionality of the effect being studied, it has no impact on the significance of the difference between groups of data.
The three main types of t-test are independent sample t-test, paired sample t-test, and one sample t-test. An independent samples t-test compares the means for two groups. A paired sample t-test compares means from the same group at different times – one year apart, for example. A one sample t-test tests the mean of a single group against a known mean.
The t-score is a ratio of the difference between two groups and the difference within the groups. The larger the t-score, the more difference there is between groups. The smaller the t-score, the more similarity there is between groups. For example, a t-score of 3 means that the groups are three times as different from each other as they are within each other. When you run a t-test, the bigger the t-value, the more likely it is that the results are repeatable.
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In simple terms, a large t-score tells you that the groups are different, and a small t-score tells you the groups are similar.
Calculating difference between group means involves subtracting one mean from the other.
Calculate the standard error of difference (also known as variability) by subtracting the mean of one group from a unique sample in that same group, squaring that value, and dividing the value by the total number of samples in the group minus 1. Perform this calculation for each unique sample and then add all the values together.
Find a t-value by dividing the difference between group means by the standard error of difference between the groups.
A negative t-value indicates a reversal in the directionality of the effect, which has no bearing on the significance of the difference between groups. Analysis of a negative t-value requires examination of its absolute value in comparison to the value on a table of t-values and degrees of freedom, which quantifies the variability of the final estimated number. If the absolute value of the experimental t-value is smaller than the value found on the degrees of freedom chart, then the means of the two groups can be said to be significantly different.