Obtain two independent data sets for a specific variable that are measured on the same scale. For example, the heights of a group of men and women measured in inches could be tested to determine if there is a significant difference in a study population.
Calculate the mean of each respective data set. The mean is calculated as the sum of the values divided by the count of values.
Mean of x variables = (x1+x2+x3...)/n, where n is the number of x variables
Calculate the variance of each data set. The variance is a measure of the spread of the values in a data set and is calculated by subtracting the mean of the data set from each individual value, squaring each resulting difference, finding the sum of the squared values and then dividing the resulting sum by the count, or number of variables in the data set. Additional help for calculating variance is provided by the Datedial and Changingminds websites.
Find the standard error between the two data sets using the calculate variances. The standard error is calculated by dividing each variance by the number of values in each respective data set, adding the two resulting values and taking the square root.
Standard Error = sqrt( [variance of x/count of x] + [variance of y/count of y])
Calculate the t-value. This is done by subtracting the calculated mean of each group and dividing this value by the standard error of the data set.
t = (mean of x -- mean of y)/ standard error
Determine the degrees of freedom for the test. The degrees of freedom is equal to two times the number of values in each data set minus two.
degrees of freedom = 2n -2
Determine the confidence level, or alpha, for the test. For most research studies, a 95 percent confidence level is used. This means that only 5 percent of resulting data would possibly be due to chance alone. The alpha value for a 95 percent confidence level is 0.05.
Use the degrees of freedom and alpha of the test to determine the p-value. This is done by looking on a statistics table found in many statistics text books and online. The table is arranged so a critical value is located in the table that corresponds to the alpha value and degrees of freedom. If the calculated t-statistic is greater than the corresponding critical value, the two data sets are considered to be significantly different.