The independent, or unpaired, t-test is a statistical measure of the difference between the means of two independent and identically distributed samples. For example, you may want to test to determine if there is a difference between the cholesterol levels of men and women. This test computes a t value for the data that is then related to a p-value for the determination of significance. One of the most recognized statistical programs is SPSS, which generates a variety of test results for sets of data. You can use SPSS to generate two tables for the results of an independent t-test.
Group Statistics Table
Find the Group Statistics Table in the data output. This table reports general descriptive statistical values such as mean, standard deviation, etc.
Interpret the N values as the number of samples tested in each of the two groups for the t-test. For example, comparing the cholesterol levels of 100 men and 100 women would have two N values of 100 and 100, respectively.
Find the standard deviation values and relate them to the data sets. The standard deviation identifies how close the set of data points within each test group are to their respective means. Thus, a higher standard deviation signifies that the data is more spread out over a wide range of values as compared to a smaller standard of deviation.
Observe the standard error mean value for the two test groups. This value is calculated from the standard deviation and sample size of the population and identifies the precision of the mean of each sample. A smaller standard error indicates that the mean is more likely to be that of the true population.
Independent Samples Test Table
- SPSS statistical program
- Two independent normally distributed data sets to test
Ensure that your two data sets are both normally distributed or the results may not be valid. This can be checked using a Normality Test in SPSS to see if the data set fits a standard bell curve.
Find the Independent Samples Test Table in the data output. This table gives the actual results from the t-test.
Check to determine if the variance in the two test groups are similar. This is done by looking at the results of Levene’s Test for Equality of Variances that is given within the table. Equal variances will be denoted with a p-value (denoted as “Sig”) greater than 0.05 (p>0.05), while unequal variances will display a p-value less than 0.05 (p<0.05).
Choose which column of numbers you need to use based on whether you have equal or unequal variances.
Identify the p-values in “t-test for Equality of Means” section of the table to determine significance. The column is denoted as “Sig. (2-tailed)”. Most studies are performed on a 95% confidence interval; thus, a p-value less than 0.05 is to be taken as significant meaning that there is a significant difference in the means of the two sample populations tested (i.e. there would be a significant difference in the cholesterol levels of men compared to women in our previous example).
Observe the 95% Confidence Interval of the Difference section of the table. This value gives an interval for which, with 95% certainty, you would predict the difference in the actual population to be based on your results. Thus, a narrower confidence interval provides more conclusive results and a better estimation of the actual population than a broader confidence interval.
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