Explain and Execute Statistical Design and Analysis of Two Variable Hypothesis - Statswork

1. EXPLAIN AND EXECUTE STATISTICAL DESIGN AND ANALYSIS OF TWO VARIABLEHYPOTHESIS An Academic presentationby Dr. Nancy Agens, Head, Technical Operations, Statswork Group www.statswork.com Email:info@statswork.com

2. TODAY'SDISCUSSION Outline ofTopics Finding a Suitable TestStatistics Calculation Of Test Statistic Conclusion of theProblem Introduction Understanding the Problem Statement Construction of TestHypotheses

3. Introduction In this blog, I will explain you how the statistical analysisis being applied for two independentsamples. In practice, the test statistic used for comparing the two means from a population is by using the t-test because t-testshrinks the data to a single t- value and it is then compared with the significant value for the finalconclusion. Now, Let us understand the theoretical background in performing the t-test for twovariables. Contd..

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5. Imagine a marketing company has recently launched twocampaigns for advertising theirproduct. The company’s head wants to identify whether both the campaignis equally effective ornot. In such case, the statistical hypothesis testing is the essentialmethod to give a validinference.

6. Understanding the Problem Statement The primary or basic task in any statistical data analysisis to know or find out what the problem is and how the data is beingmeasured. In our example, the manager wish to find the effectiveness of their campaign, for this, he/she has to consider all the information related to the campaign and find out whether the campaign results in a profit orloss. The only way to test whether the two campaign is effective is to perform a statistical test by comparing theirmeans.

7. Construction of TestHypotheses Once youunderstandthe problem at hand, the next step is to frame an appropriate hypothesisto test for statistical significance; we call it as the null hypothesis and alternativehypothesis.

8. Finding a Suitable TestStatistics For finding the suitable statistic test, we need to find the distribution of the data. I will illustrate with a simulated data for two campaigns using Rsoftware. set.seed(123) camp1<-rt(30,29)*50+210 camp2<-rt(30,29)*48+170 If you see the Below graph, the data is closely resembles a normaldistribution. From the simulated data, the mean for two campaigns is $210.2226 with standard deviation $60.0008 and $182.8537 with standard deviation $47.56557respectively.

9. Figure 1 Histogram-NormalDistribution

10. Calculation Of TestStatistic Once you got all the necessary values for the calculation, the next step is to apply it into the formula of statistics testas mentioned earlier. Here, I will illustrate usingR.

11. Conclusion of theProblem As a final step, we compare the calculated t.value with the criticalvalue. In order to find the critical value, we need to fix the significance levelalpha. Usually, it is considered as 5% that means we can tolerate the probability of rejecting the nullhypothesis by 5% or 0.05 level ofsignificance. Next step is to check whether the null hypothesis is one-sided or two-sided for concluding the problem. If you are concerned about which campaign is higher or smaller then the null will beone-sided. However, in our case, it is two sided null hypothesis stating that the means of the campaigns areequal. An important note is that in a two-sided test the critical region is divided by half (5% is equally distributed in both sides from populationmean). Contd..

12. In R, there is a function called t.test to perform the calculation and the p-value is compared with 0.05 for the conclusion. From the results, the t-value (or test statistic) is 1.9578 as we got previously and the p-value is 0.05507, which is greater than0.05. Since the p-value is greater than 0.05, we accept the null hypothesis and conclude that the difference of mean amount from two campaign issame.

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