EXPLAIN AND EXECUTE STATISTICAL DESIGN AND ANALYSIS OF TWO VARIABLE An Academic presentation by HYPOTHESIS Dr. Nancy Agens, Head, Technical Operations, Statswork Group
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TODAY'S DISCUSSION Outline of Topics
Introduction
Finding a Suitable Test Statistics
Understanding the Problem Statement Construction of Test Hypotheses
Calculation Of Test Statistic Conclusion of the Problem
Introductio nIn this blog, I will explain you how the statistical analysis is being applied for two independent samples. In practice, the test statistic used for comparing the two means from a population is by using the t-test because t-test shrinks the data to a single tvalue and it is then compared with the significant value for the final conclusion. Now, Let us understand the theoretical background in performing the t-test for two variables. Contd..
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Imagine a marketing company has recently launched two campaigns for advertising their product. The company’s head wants to identify whether both the campaign is equally effective or not. In such case, the statistical hypothesis testing is the essential method to give a valid inference.
Understanding the Problem Statement
The primary or basic task in any statistical data analysis is to know or find out what the problem is and how the data is being measured. 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 or loss. The only way to test whether the two campaign is effective is to perform a statistical test by comparing their means.
Construction of Test Hypotheses Once you understand the problem at hand, the next step is to frame an appropriate hypothesis to test for statistical significance; we call it as the null hypothesis and alternative hypothesis.
Finding a Suitable Test Statistics
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 R software. 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 normal distribution. From the simulated data, the mean for two campaigns is $210.2226 with standard
Figure 1 Histogram-Normal Distribution
Calculation Of Test Statistic Once you got all the necessary values for the calculation, the next step is to apply it into the formula of statistics test as mentioned earlier. Here, I will illustrate using R.
Conclusion of the Problem As a final step, we compare the calculated t.value with the critical value. In order to find the critical value, we need to fix the significance level alpha. Usually, it is considered as 5% that means we can tolerate the probability of rejecting the null hypothesis by 5% or 0.05 level of significance. 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 be one-sided. However, in our case, it is two sided null hypothesis stating that the means of the campaigns are equal. 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 population mean).
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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 than 0.05. 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 is same.
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