Question

Question 1. My student union poll included another question regarding the preference for different dog breeds. I find that there is a statistically significant association between preferred dog breeds and gender of the students. I calculate a Cramer's V test and get a result of 0.05. What conclusion would I make about this result?

A) The Cramer's V score disproves our statistical significant finding.

B) The result was statistically significant, but not substantively significant.

C) The Cramer's V value further proves that the result is significant.

Question 2. I decide to conduct another poll outside the student union, and I want to ensure that my poll will have a low probability of Type II error and will be able to detect a difference with a medium effect size. I run the following code:

pwr.chisq.test(w = 0.3, N=NULL, df = 20, sig.level = 0.05, power = 0.8)

I get the following output in R:

Chi squared power calculation

w = 0.3
N = 232.8977
df = 20
sig.level = 0.05
power = 0.8

What does this output tell me about how I need to design my next poll.

A) I need a sample size of 233 students to obtain a result with the power I desire to have in my analysis.

B) Since I set my sample size at 233 I will achieve a power of 0.8.

C) A sample size of 230 should be sufficient for my poll.

D) My new poll needs a power of 0.8 to have an effect size of 0.3.

Question 3. Which of the following reflects the substantive significance of a statistic?

A) effect size

B) p-value

C) beta

D) alpha

Answer 1

Cramér's V:

In statistics, Cramér's V is a measure of association between two nominal variables, giving a value between 0 and +1 (inclusive).

The Cramer's V statistic doesn't show direction. On a 2 x 2 table, phi shows direction with positive or negative sign, but directionality doesn't make much sense in a larger table of nominal categories.

There is no absolute interpretation of an effect size statistic like Cramer's V. It is always relative to the discipline and the expectations of the experiment.

Statistical significance reflects the improbability of findings drawn from samples given certain assumptions about the null hypothesis.

Substantive significance is concerned with meaning, as in, what do the findings say about population effects themselves?

1) Suppose  Cramer's V test is  0.05 then

C) The Cramer's V value further proves that the result is significant.

2)  

Chi squared power calculation is

w = 0.3
N = 232.8977
df = 20
sig.level = 0.05
power = 0.8 then,

C) A sample size of 230 should be sufficient for my poll.

3)

Substantive significance refers to whether an observed effect is large enough to be meaningful. The concept of substantive significance was developed because statistical SIGNIFICANCE TESTS can find that very small effects are significant.

reflects the substantive significance of a statistic is

A) effect size