Explain the difference between the information given by the

Explain the difference between the information given by the tests of statistical significance t and Chi Square, and measures of association Cramer’s V, Gamma and Pearson’s correlation coefficient, r.

Can a test of significance show a statistically significant relationship while a measure of association shows a weak relationship between the variables?

If yes, present an example illustrating how such a situation might occur.

Solution

I would like to help you with all of your question but Chegg\'s policy allow me to answer only the first question

first we need to know what tell us the tests of statical sifnifcance?

Tests for statistical significance tell us what the probability is that the relationship we think we have found is due only to random chance. They tell us what the probability is that we would be making an error if we assume that we have found that a relationship exists.

CHI SQUARE

steps:

1) display observed frequencies for each cell
2) calculate expected frequencies for each cell
3) calculate, for each cell, the expected minus observed frequency squared, divided by the expected frequency
4) all up the results for all the cells

T TEST

steps:

a) state the research hypothesis;
b) state the null hypothesis;
c) stipulate whether the t-test will be a one-tailed test or a two-tailed test for significance
d) select the level of alpha
e) calculate t

as we can see the difference is that the t test not use an observed frequencies and expected frequencies

in t test you just have 1 frequency that is the data with you will calculate the mean and standard deviation

in chi squares you use other formula that needs expected and observed frequencies to calculate this test

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Cramer’s V, Gamma and Pearson’s correlation coefficient, r.

Cramer\'s V This coefficient is used with nominal variables

Correlation appropriate for continuous and discrete variables

Gamma () use when you have two ordinal measures like Kendall’s Tau