# 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

 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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