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STUDENT T - TEST
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-TEST
1. 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?
HOW TO CONDUCT A T-TEST
1. Calculate the t-statistic:
Each type of t-test has a different formula for calculating the t-statistic (You can scroll to the
bottom of the page to find all three formulas).
2. Calculate the degrees of freedom:
Degrees of freedom are the number of ways the mean could vary. In this case, the degrees of
freedom are the number of NPS ratings that you could have in a given group of respondents.
Similar to the t-statistic, the formula for degrees of freedom will vary depending on the type of
t-test you perform.
3. Determine the critical value:
The critical value is the threshold at which the difference between two numbers is considered
to be statistically significant.
4. Compare absolute value of the t-statistic to critical value:
If your t-statistic is larger than your critical value, your difference is significant. If your t-
statistic is smaller, then your two numbers are, statistically speaking, indistinguishable.
CALCULATE T-STATISTIC
Below is the formula for the two-sample t-test, where:
t is the t-statistic
x1 is the average NPS for men → 9
x2 is the average for women → 12
n1 is the number of men who provided a response to the NPS question → say 20 men
responded to the survey
n2 is the number of women → 23 women responded
s1 is the standard deviation of the NPS for men → say the calculated standard deviation is
12.48
s2 is the standard deviation of the NPS for women → the calculated standard deviation is
10.51
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.
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.
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.
Student T -  test
Student T -  test
Student T -  test

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Student T - test

  • 1. STUDENT T - TEST
  • 2. 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.
  • 3. THE THREE MOST COMMON TYPES OF T-TEST 1. 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?
  • 4. HOW TO CONDUCT A T-TEST 1. Calculate the t-statistic: Each type of t-test has a different formula for calculating the t-statistic (You can scroll to the bottom of the page to find all three formulas). 2. Calculate the degrees of freedom: Degrees of freedom are the number of ways the mean could vary. In this case, the degrees of freedom are the number of NPS ratings that you could have in a given group of respondents. Similar to the t-statistic, the formula for degrees of freedom will vary depending on the type of t-test you perform. 3. Determine the critical value: The critical value is the threshold at which the difference between two numbers is considered to be statistically significant. 4. Compare absolute value of the t-statistic to critical value: If your t-statistic is larger than your critical value, your difference is significant. If your t- statistic is smaller, then your two numbers are, statistically speaking, indistinguishable.
  • 5. CALCULATE T-STATISTIC Below is the formula for the two-sample t-test, where: t is the t-statistic x1 is the average NPS for men → 9 x2 is the average for women → 12 n1 is the number of men who provided a response to the NPS question → say 20 men responded to the survey n2 is the number of women → 23 women responded s1 is the standard deviation of the NPS for men → say the calculated standard deviation is 12.48 s2 is the standard deviation of the NPS for women → the calculated standard deviation is 10.51
  • 6.
  • 7. 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.
  • 8. 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.
  • 9. 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.