Week 7

Research in Public Administration
Supplemental Materials

menu

project

Topic and Activities

Assignment

THIS WEEK: NON PARAMETRIC DATA ANALYSIS

Ordinal Data
Overview

1.      Example of Scales
2.      Picking the Appropriate Statistic
3.      Looking at output

Nominal Data
Overview

1.      Picking the Appropriate Statistic
2.      Looking at output

See materials below

NEXT WEEK: Sharing Research With Others

1.      On-Going Communication
2.      Format of the Report
3.      Presentation

SPSS Demo

Ordinal Data

Overview

We think of numbers as intervals or unit measurements such as age in years.
But, we often don’t have an instrument than can measure variables in unit terms. The next best option is to find or develop ordinal measures.
There are several indices and scales social scientists have used such as the Likert and Guttman scales. [these are examples only, not a complete list.]

Scale Defined

Likert scale	Present a statement and ask the respondent if she/he strongly disagrees, somewhat disagrees, somewhat agrees, strongly agrees or has no response.
Example of Likert	I agree with American foreign policy. 1. strongly disagree, 2 somewhat disagree, 3. somewhat agree, 4. strongly agree or 5. no response.
Guttman	Ask a respondent from a scale of increasing intensity to select the statements they agree with.
Example of Guttman scale.	___I have run for a local elected office ___I have worked on a political campaign for local office. ___I have contributed money to a local political campaign ___I have voted in a local election. ___I am a registered voter The response to “run” for office represents the greatest commitment to local politics and would probably indicate the person would “agree with” all 5 statements. The respondent who only agrees with “I am a registered voter” probably is not committed to local politics (1). The numbers identify relative position NOT an absolute unit difference.
Types of Ordinal	a. Forced choice where items are ranked from most to least with few “tie” scores (two or more having the same position). b. Less precise ‘categorical’ scales such as the Likert and Guttman scales described earlier. Here the distribution of the data would be displayed using cross tabs

2. As with interval ratio data, there are different tests for different questions the researchers asks .

If the researcher is asking----	When data is interval ratio ($)	Ordinal [interval-like array] Definitions of tests	Ordinal [cross tab like array] Definitions of tests SCROLL TO CROSS TAB TABLE DEF.
Are 2 categorical groups, such as men v. women equal with regards to a variable e.g. success?	t-test (groups)	Mann/Whitney U	*see note below
Are 3 or more categorical groups (e, g. Anglos, Asians, Hispanics) equal to one another with regard to a variable e.g. success?	ANOVA	Kruskal Wallis (each subgroup must have at least 6 observations) OR Friedman test (need 10 observations/category)	*see note below
Is there a difference between the before and after for a variable such as success?	t-test (pairs)	Median Score Or Wilcoxon Rank	*see note below
Does the independent variable (information) significantly influence the dependent variable (success)?	Pearson and Linear Regression	Spearman’s Rho	Gamma *** Kendall’s tau c Kendall’s tau b Somer’s D
Do multiple independent variables significantly influence the dependent variable (success)?	Pearson’s and Multiple Regression	**	n.a.
*NOTE: You can use a chi-square (pronounced “ki”) test to determine if different categorical groups (2 or more) display different distributions of responses from one another. This is a correlation test indicating if the relationships between the groups are what one would expect at random. The chi square will not indicate if the probability of the categorical differences improves the researcher’s ability to predict. The researcher would also have to use a proportional reduction in error (PRE) test such as a tau. From Levin and Fox Elementary Statistics
**This analysis is more complicated and beyond the scope of this introductory course.
*Gamma test does not adequately account for tie scores so it may indicate statistical significance prematurely. Kendal’s tau is a more precise test. Kendal tau-b is used when the number of rows (R) equals the number of columns (C) in the cross tab. Kendal’s tau c** is used when the number of R does not = C. Somer’s D is a more conservative test than Kendal’s tau-b and may indicate no or a low statistically significant relationship that in fact is higher.

3. Below are some interactive examples of how to run and read output from these tests.

If the researcher is asking----	Ordinal [interval-like array]	On Line Applet
Are 2 categorical groups, such as men v. women equal with regards to a variable e.g. success?	Mann/Whitney U	(on line test compliments of OBGYN in Hong Kong)
Are 3 or more categorical groups (e, g. Anglos, Asians, Hispanics) equal to one another with regard to a variable e.g. success?	Kruskal Wallis (each subgroup must have at least 6 observations) OR Friedman test (need 10 observations/category)	on line Kruskal Wallis (from OBGYN in Hong Kong) On line Friedman from phonetic course in the Netherlands.
Is there a difference between the before and after for a variable such as success?	Median Score Or Wilcoxon Rank	Median Score and Wilcoxon Paired Match from phonetic course in the Netherlands.
Does the independent variable (information) significantly influence the dependent variable (success)?	Spearman’s Rho	On-line test from OBGYN in Hong Kong
Does the independent variable (information) significantly influence the dependent variable (success)?	Gamma *** Kendall’s tau c Kendall’s tau b Somer’s D	Chi Square from the physics department of St. Benedict's College in St. John's University of Minnesota.
Do multiple independent variables significantly influence the dependent variable (success)?	** [not addressed in this discussion]	N.A.

4. Looking at output and developing findings.

When using a Chi square, gamma, tau or Somer’s D display the cross tabs.
Indicate “row” percentages in the cross tab cells.
The traditional presentation with cross tabs is to make the columns the independent (or grouping) designation and the rows the dependent variable.
Report the “df” or degrees of freedom. It helps the reader understand how big the cross tab table was.
The reader may be interested in the statistics value e.g. U in the Mann Whitney U,
The critical piece of information is the “p” value. The probability of error.

Nominal Data

Overview

The least specific and least accurate data is nominal data. Here the number represents a name. Because it is imprecise there is little mathematical manipulation one can do with it.

1. Picking an appropriate statistic

a. Yule’s Q (ad-bc/ad+bc) can only be used for nominal data distributed on a 2X2 table.

b. Chi square which can be used to test association on larger cross tabs with many rows and many columns. However the Chi square requires no fewer than 5 observations in any cell.

c. The Kruskal tau measures the strength of the relationship between two nominal level variables. Some statisticians prefer the Kruskal tau to the Chi square. Kruskal tau should be used in conjunction with the chi-square.

3. Looking at output.

The reporting is the same as for ordinal.
Indicate the test used, value computed, degrees of freedom (DF) and
the “p-value” or probability of error. .05 or less is considered statistically significant
a statistically significant finding indicate the researcher will reject the null hypothesis.