Question

When politicians make claims that we need to spend a large amount of money to achieve a goal, the claim is often made without legitimate evidence to support a claim that a given program will have a particular result. Let's say that a politician wants to implement a nation-wide education program. The politician gave four examples of schools that used the program: scores at the schools increased 0.5, 1, 2, and 2.5 points respectively (the nation-wide average of the scores is 70). The politician gave no additional evidence about the effectiveness of the program.

Your task: What questions or comments would you have pertaining to the statistical claim made by the politician? You might inquire about the sample, the sampling methods, the full population, the sampling distribution of the mean, and whatever would be useful to more accurately or precisely describe the effectiveness of the program. At the end of your post, state whether you would conclude that the program will increase scores nation-wide.

Note that it is a separate question of whether it is "worth it" to effect change by taking money from people in the form of taxes to pay for a program. Other than (optionally) saying that you think the statistics can or can not answer such a question, the "worth it" question is not part of this discussion.

Answer 1

First we define the purpose and objectives of the study.

Here we want to test the effectiveness of the programme.

Now we need to define the sampling units for the selection of it.

For the above case the sampling units is the individual students.

Then we collect the information of GPA .

If whole of the population that is all the students in the area under study is included in the sample then we conclude that the gPA increase as 0.5, 1, 2, 2.5 and the program is effective.

If all the students are not included in the survey then we need to examine the following different aspect of the study.

1. The method of selection of sample:

If the sample select randomly then unbiaed result are obtained from the sample data. But the selection of sample without using the random sampling techniques then the biased results are obtained. Such biased sample may result the increase in the GPA, but actually it may not.

2. Sample size is one of the things to examine the significance of the increase in the average.

If sample size is very large then the small changes in the average indicates the mean is statistically significance. So in this case we need to find the effect size of the test. Using the effect size we can conclude the result is also practically significance or not.