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T-tests explained: what they mean for survey analysisAre there statistically significant differences in your data? Analyzing survey results is sometimes more involved than simply comparing bar graphs.While anyone can see the difference between two numbers, finding out whether that difference is actually statistically significant can take a little more work.
Let’s say you’ve run a customer satisfaction survey for your company, and you’ve got loads of results to analyze. You ask your boss what to analyze first and she says she wants to know if men and women give different responses. For example, do men on average give your company a lower Net Promoter Score℠ (NPS) than women? When you dig into the data, you see that the average rating from male respondents was 9, compared to an average score of 12 from female respondents. How do you know if 9 is significantly different from 12? That’s where the t-test comes in. The t-test is a way to determine whether two numbers are significantly different from one another. There are several types of t-test, and each is calculated using a different formula.
The three most common types of t-test1. One-sample t-test: This test looks at whether the mean (aka average) of data from one group (in this case the overall NPS) is different from a value you specify. Example: Your company’s goal is to have an NPS that’s significantly higher than the industry standard of 5. Your company’s latest survey puts its NPS at 10. Is an NPS of 10 significantly higher than the industry standard of 5? 2. Two-sample t-test: This test examines whether the means of two independent groups are significantly different from one another. Example: Your hypothesis is that men give your company a lower NPS than women.The average NPS from male respondents is 9, while the average score from women is 12. Is 9 significantly different from 12? 3. Paired t-test: This test is for when you give one group of people the same survey twice. A paired t-test lets you know if the mean changed between the first and second survey. Example: You surveyed the same group of customers twice: once in April and a second time in May, after they had seen an ad for your company. Did your company’s NPS change after customers saw the ad? Note that while t-tests can tell you if something is significantly different, it’s up to you to determine whether that difference is meaningful. Small differences can be statistically different if the sample size is large enough. How to conduct a t-testThere are 4 steps to conducting a t-test: 1. Calculate the t-statistic: 2. Calculate the degrees of freedom: 3. Determine the critical value: 4. Compare absolute value of the t-statistic to critical value: Pulling it all togetherLet’s walk through the example from the beginning: Your hypothesis is that men give a lower NPS to your company than women. The average NPS from men is 9, while the average score for women is 12. Is 9 significantly different from 12? This is an example of where to use the two-sample t-test. 1. Calculate t-statistic: Below is the formula for the two-sample t-test, where:
 2. Calculate the degrees of freedom: This formula must be used to determine degrees of freedom in two-sample t-tests. The formulas for other types of test are included below. 3. Determine critical value: According to this table, for a two-tailed test with an alpha level of 0.05 at 41 degrees of freedom, the critical value is 2.02. Note that most analysts use a two-tailed test instead of a one-tailed test because it’s more conservative. For more information on the differences between one-tailed and two-tailed tests, check out this video from Khan Academy. 4. Compare absolute value of the t-statistic to critical value: Since the absolute value of the t-statistic is 0.86, which is not larger than the critical value of 2.02, then you can conclude that men do not give a significantly lower NPS ratings than women. Formulas for other t-testsYou’ll probably be conducting the t-tests in a spreadsheet or statistical program (like Excel or SPSS), but if you’d like to do the math by hand, the formulas for the other two types of t-tests are included below. If you decide (as most people do) to conduct t-tests in a spreadsheet or statistical program, the process will be slightly different. Instead of comparing the t-statistic to the critical value, most programs calculate a p-value, which it compares to your alpha level (the most commonly used level is 0.05). In this case, a p-value lower than your alpha level will show that the numbers are significantly different. Net Promoter Score is a trademark of Bain & Company, Inc., Satmetrix Systems, Inc. and F. Reichheld. See how SurveyMonkey can power your curiosityHow do you determine if there is a significant difference between two groups?If the means of the two groups are large relative to what we would expect to occur from sample to sample, we consider the difference to be significant. If the difference between the group means is small relative to the amount of sampling variability, the difference will not be significant.
What type of statistical test would you use to determine if there is a significant difference between the enzyme activity 2 bacteria?The unpaired T-test would be used to determine if there is a significant difference between the control and treated enzyme activities.
Which statistic is used to determine if there is a significant difference between two sets of related scores?The Students T-test (or t-test for short) is the most commonly used test to determine if two sets of data are significantly different from each other.
What test can be used to test if there is a significant difference between the two experimental groups?The dependent t-test (also called the paired t-test or paired-samples t-test) compares the means of two related groups to determine whether there is a statistically significant difference between these means.
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