A 12-month email study looked
The situation…
• A 12-month email study looked at the click-through responsestriggered by two versions of email, Version A and Version B.
• In all 24 distributions (12 for Version A; 12, Version B)emails were drawn randomly.
• People receiving A or B versions were unrelated (randomlyselected every time for both version of the email).
• The researchers had no idea which version would trigger moreclicks.
• Alpha was set at p <.05.
| MONTH | Group A | Group B |
| January | 36 | 36 |
| February | 35 | 25 |
| March | 24 | 29 |
| April | 23 | 37 |
| May | 29 | 37 |
| June | 12 | 23 |
| July | 18 | 27 |
| August | 12 | 21 |
| September | 14 | 24 |
| October | 24 | 33 |
| November | 25 | 32 |
| December | 33 | 40 |
| Mean | ||
| SD | ||
| Variance | ||
| t test | ||
| Effect Size | ||
Answer:
| MONTH | Group A | Group B |
| January | 36 | 36 |
| February | 35 | 25 |
| March | 24 | 29 |
| April | 23 | 37 |
| May | 29 | 37 |
| June | 12 | 23 |
| July | 18 | 27 |
| August | 12 | 21 |
| September | 14 | 24 |
| October | 24 | 33 |
| November | 25 | 32 |
| December | 33 | 40 |
| Mean | 23.75 | 30.33333 |
| StandardDeviation | 8.508018 | 6.372288 |
Two sample ttest is used to compare the means assumingequal variance. The test is performed in followingsteps,
Step 1: The Null and Alternative Hypotheses
Step 2: Select the appropriate test statistic and level ofsignificance.
The t statistic is used to compare the two populationmeans and the significance level is for the test 
(Generally 5% significance level used to compare two means)
Step 3: State the decision rules.
The decision rules state the conditions that if,
,
Step 4: Compute the appropriate test statistic and make thedecision.
The t statistic is used to compare the two populationmeans. The t statistic is computed using the formula,
The P-value for the t statistic is obtained using the tdistribution table for degree of freedom = n -1 = 24 -1 = 23,
Decision:
The corresponding P-value is 0.06 which is less than 0.05 at the5% significance level for the two sided alternative hypothesis.
Step 5: State the Conclusion
The null hypothesis is rejected. Hencethere is a statistically significant evidence that the Group 1 hasless click-through responses ( t value is negative)
The effect size is obtained by using the formula,
Cohen’s d value, d=0.2 considered a ‘small’effect size, 0.5 represents a ‘medium’effect sizeand 0.8 a ‘large’ effectsize
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