# we’ll use tests of “measures of association” to figure out the exact strength of a relationship between two variables.

Textbooks

1. OpenStax, Introductory Statistics. OpenStax. 19 September 2013. http://cnx.org/content/col11562/latest/

2. Tyrrell, S. 2009. SPSS: Stats practically short and simple (1st edition). bookboon.com. Ebooks and textbooks from Bookboon.com https://oerstatistics.wordpress.com/2016/03/05/spss-books/

Original Question:

In week 3, we used epsilons and 10-percent-point rule to determine if a potential relationship between two variables is worth examining further.

This week, we’ll use tests of “measures of association” to figure out the exact strength of a relationship between two variables. In addition, we’ll learn how to interpret SPSS outputs for measures of association tests such as lambda, gamma, and Pearson’s r， along with other possible tests.  Remember that these tests are specific to the level of measurement that your variables are.  In other words, one test may not work in a different relationship test. Here are the guidelines:

1. Both DV and IV are nominal variables: Lambda (when it is not a 2X2 table)

a. If it is a 2X2 table: Phi

2. Both DV and IV are ordinal variables: Gamma

3. One variable ordinal AND the other variable dichotomous nominal (like Yes/No, male/female, etc.): Gamma

a. One variable ordinal AND the other variable nominal (not dichotomous, has more than 2 categories): Cramer’s V.

4. Both DV and IV are I/R variables: Pearson’s r

To interpret the output:

Keep in mind measures of association is a statistical procedure based on Proportional Reduction of Error (PRE). Thus the format of interpretation will be:

……knowing the IV will reduce error in predicting the DV by *%.

Please note: Don’t just say “IV” and “DV” in your explanation. You need to enter your variables names for IV and DV, and replace * for the exact test value from the output. If the value of Lambda is .34, then it will be interpreted as 34%.

Ok, now it is time for you to try! Be sure to test the strength of association of your final project for this week’s forum discussion. You can download the class handout attached at the bottom of the page, or  Click here for details.

Reply to the following response with 200 words minimum. (please make response as if having a conversation, respond directly to some of the statements in below post.)

Crosstabs w/Gamma & Lamda

Hello Dr T. & Fellow Classmates,

Well, things are not looking good, as far as establishing some sort of relationship between my two variables: Capital Punishment & Marital Status. But here are the results that I got when I ran them.

Cappun & Marit

 Directional Measures Value Asymptotic Standard Errora Approximate T Approximate Significance Nominal by Nominal Lambda Symmetric .000 .000 .b .b cappun FAVOR OR OPPOSE DEATH PENALTY FOR MURDER Dependent .000 .000 .b .b marital MARITAL STATUS Dependent .000 .000 .b .b Goodman and Kruskal tau cappun FAVOR OR OPPOSE DEATH PENALTY FOR MURDER Dependent .017 .006 .000c marital MARITAL STATUS Dependent .006 .002 .000c a. Not assuming the null hypothesis. b. Cannot be computed because the asymptotic standard error equals zero. c. Based on chi-square approximation

Using the original Martial variable, we get the big goose-egg, suggesting that there is not any relationship between these two variables.

 Symmetric Measures Value Asymptotic Standard Errora Approximate Tb Approximate Significance Ordinal by Ordinal Gamma .144 .038 3.683 .000 Spearman Correlation .087 .024 3.742 .000c Interval by Interval Pearson’s R .093 .024 3.998 .000c N of Valid Cases 1824 a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis. c. Based on normal approximation.

The Gamma result is not showing any better result, suggesting that flipping a coin might be a more reliable predictor as to whether someone’s marital status has any effect upon their position concerning capital punishment. The Pearson’s R falls in the .01-.09, no association at all category.

Cappun & NMar

 Directional Measures Value Asymptotic Standard Errora Approximate T Approximate Significance Nominal by Nominal Lambda Symmetric .000 .000 .b .b cappun FAVOR OR OPPOSE DEATH PENALTY FOR MURDER Dependent .000 .000 .b .b Nmar Marsat Dependent .000 .000 .b .b Goodman and Kruskal tau cappun FAVOR OR OPPOSE DEATH PENALTY FOR MURDER Dependent .013 .006 .000c Nmar Marsat Dependent .013 .006 .000c a. Not assuming the null hypothesis. b. Cannot be computed because the asymptotic standard error equals zero. c. Based on chi-square approximation

Which again, via the Lambda results, gives us yet another naught reading.

 Symmetric Measures Value Asymptotic Standard Errora Approximate Tb Approximate Significance Ordinal by Ordinal Gamma .243 .055 4.185 .000 Spearman Correlation .116 .028 4.263 .000c Interval by Interval Pearson’s R .116 .028 4.263 .000c N of Valid Cases 1333 a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis. c. Based on normal approximation.

The Gamma result here is slightly improved, likely by the fact that it is truly a dichotomous nominal (only two variables in my N-Mar, as opposed to the multiple response choices in Marit variable.) It has a result of .05 (.243 x .243)

The Pearson’s R brings us up a bit as well, into the + or – .10 to .29 (Moderate association area.)

And that is what I have for this week.

Allyn

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