TTEST

Returns the result of a Student's t-test.

Syntax:

TTEST(data1, data2, mode, type)

data1 and data2 are ranges or arrays (possibly of different size) containing numbers, on which the t-test is performed.

mode is

  1 for a one-tailed t-test

  2 for a two-tailed t-test.

type is

  1 for paired samples

  2 for two samples with equal variance

  3 for two samples with unequal variance.

Example:

TTEST(A2:A20, B2:20, 2, 3)

returns the result of a two-tailed Student's t-test for two samples with unequal variance, using the data in A2:A20 and B2:20.

The Hypothesis

• Null Hypothesis (H0​): There is no significant difference in the average number of clicks between Campaign A and Campaign B. Any observed difference is due to random chance.
• Alternative Hypothesis (H1​): There is a significant difference in the average number of clicks between Campaign A and Campaign B. Campaign B is more effective.

Using the T.TEST Function

The T.TEST function would be used to calculate the p-value. The syntax for the function is generally:

T.TEST(array1, array2, tails, type)

• array1: The range of data for Campaign A (e.g., B1:B7).
• array2: The range of data for Campaign B (e.g., C1:C7).
• tails: This specifies the type of test.
• • 1 for a one-tailed test (used if you have a directional hypothesis, e.g., "Campaign B is better than Campaign A").
  • 2 for a two-tailed test (used if you are just testing for a difference in either direction, e.g., "Is there a difference between the two campaigns?"). In this case, we would use a one-tailed test with tails = 1.
• type: This specifies the type of t-test.
• • 1 for paired t-test (data points are related, e.g., before-and-after measurements on the same subjects).
  • 2 for two-sample equal variance (assuming the variances of the two data sets are roughly equal).
  • 3 for two-sample unequal variance (a more common and conservative choice, often called a Welch's t-test). For this example, we will use type = 3.

The formula would look something like this:

T.TEST(B1:B7, C1:C7, 1, 3)

Interpretation of Results

The T.TEST function will return a p-value. The function returns a p-value of 0.000098202.

A p-value is the probability of observing the data you have, assuming the null hypothesis is true. A common significance level (alpha, α) is 0.05.

• If p-value < α (0.05): You reject the null hypothesis. This means the observed difference is statistically significant.
• If p-value > α (0.05): You fail to reject the null hypothesis. This means the observed difference is likely due to random chance.

In this example, since our p-value (0.015) is less than the significance level of 0.05, we reject the null hypothesis.

Conclusion

The marketing manager can conclude that there is a statistically significant difference between the average daily clicks of the two campaigns. Based on the data, Campaign B consistently generated a higher number of clicks. Therefore, the manager should recommend continuing with the video-based advertising of Campaign B.