A single-sample t-test is used to evaluate the difference between a sample measure and a population measure (Gravetter & Wallnau, 2013). The population measure can be real or hypothesized. as noted on the Statistical Decision Tree Calculator, vCalc is not set up to allow a user to define inputs, so this test will take you through an example of a single-sample t-test using the dataset "Test scores for School of Awesomeness!" located. We are using a single-sample t-test because we are comparing one sample of test scores, the School of Awesomeness, to the national average test score.
Type of test - This question asks whether you are doing a one-tailed (directional) or two-tailed (non-directional) hypothesis test. Your critical t-value will be different depending on the type of hypothesis you are making. A one-tailed test indicates you are hypothesizing significance in a certain direction: higher, lower, more, less, etc. In our School of Awesomeness example, a directional hypothesis could be "We expect that the School of Awesomeness will have a higher average test score than the national average score." A two-tailed test, by contrast, indicates you are hypothesizing there will be a significant difference, but not predicting a direction. In our example, a non-directional hypothesis could be "We expect that the test scores for the School of Awesomeness will differ significantly from the national average test score."
Sample size - This is how many participants or subjects you used in your study. This calculator can handle sample sizes between n=5 and n=23.
M - This is the mean of your data. It is calculated by adding up every individual value from your data and dividing by the number of values (n). Using the descriptive statistics calculator for a sample of 12 located below in the "Computing Mean and Standard Deviation" section, we see the mean is 86.25.
o - This is the standard deviation. When you enter your standard deviation, the calculator will use it to determine the standard error (SE). We will calculate this for the School of Awesomeness example. Using the descriptive statistics calculator for a sample of 12 located below in the "Computing Mean and Standard Deviation" section, we see the standard deviation is 6.2541.
u - This is the population mean you are comparing your sample to. It could be given in the problem you're solving, or it could be on a reputable website. For our dataset, the u is just from our imagination - let's say we are comparing the School of Awesomeness to the national average, which is 88.
When you plug the values above into the calculator, you should receive a string that looks like this: df = 11, critical t-value = 1.796, t = -0.97 and SE value is 1.81.
The results of this calculator are your degrees of freedom (df), your critical t-value, your t (solved above for the School of Awesomeness example), and the standard error (SE). It is important to identify your critical region for your t-test so you know whether your value falls in the region of significance or non-significance. The output will deliver an accurate critical t-value that is computed based on your degrees of freedom, which is calculated from your sample size that you input.
According to the output from the School of Awesomeness example, our t-score is not above the critical t-value, which means the t-score is not significant. The test scores for the School of Awesomeness is not significantly different from the national average scores.
The following calculators provide descriptive statistics, including mean and standard deviation, for any sample size between n=6 and n=12. Choose the calculator for your sample size, enter your data, and choose the statistic you want.
Gravetter, F. J., & Wallnau, L. B. (2013). Statistics for the Behavioral Sciences. Wadsworth, CA: Cengage Learning.