Question

Background Information:

Null Hypothesis Significance Testing (NHST) has long been the workhorse of the scientific method. The procedure, familiar to us from Modules 7-9, is

1. Assume a null hypothesis
2. Calculate a test statistic
3. If the test-statistic reaches the designated significance level (alpha), reject the null hypothesis, usually in favor of the theory you propose

Despite its ubiquity, the procedure has received a fair amount of criticism. Some of these critiques are:

• We often already know the null hypothesis is unlikely to be true
• The traditional significance cutoff point of 0.05 is arbitrary
• A result may be statistically significant (especially when the sample size is large) but not practically significant

Here we will examine some of the issues that arise from an overemphasis on significance testing.

Consider a study of the effectiveness of an educational program for at-risk high school students in Florida. The goal of the program is to raise average SAT scores.

A random sample was taken of students who had been enrolled in the program for the past two semesters (Group A). Likewise, a random sample was taken of students was taken who had not ever been enrolled (Group B).

Researchers wished to assess whether students in Group A had significantly higher average SAT scores compared to students in Group B.

$LaTeX: H_0: \mu_A-\mu_B=0$ H 0 : μ A − μ B = 0

$LaTeX: H_1: \mu_A-\mu_B>0$

Question:

Part A. What type of study design is this?

a) Randomized Controlled Experiment

b) Census

c) Observational Study

d) Focus Group

Part B: Suppose the sample sizes for Group A and Group B were 160 and 250, respectively. What would be the number of degrees of freedom for the obtained t statistic in a two-sample test for means?

a) 410

b) 205

c) None of the above

d) 408

Answer 1

Part A. This is a type of observational study as the researchers in this study observe the effect of the program on the students without trying to change anything. They do not intervene in the study and just assess the information of both the groups.

Correct option: C) Observational study

Part B. The degrees of freedom for a independent samples t-test is:

df = n1 + n2 - 2

df = 160 + 250 - 2 = 408

Correct option: D) 408