Chi-Square

Parametric tests are designed to test hypotheses related to population parameters. Certain assumptions must be met to test these hypotheses. Researchers also encounter situations when statistical assumptions are violated and/or the data does not match the assumptions of parametric tests. When this occurs, non-parametric tests such as a chi-square should be used.

A chi-square analysis determines whether one variable is related to or contingent upon another variable when nominal scale data are in frequencies, proportions, or percentages. With nominal variables, an amount is not measured, but rather obtained amounts are calculated by categories.

For example, a special education director might be interested in determining the effect of a behavioral intervention technique on reducing the frequency of emotional outbursts among severely behaviorally challenged students with autism. Throughout the school district, a baseline frequency of emotional outbursts is recorded among severely behaviorally challenged students with autism, the behavioral intervention technique is then implemented for a designated amount of time, and a final frequency of emotional outbursts is recorded. A dependent-samples chi-square is then employed to compare the frequency of emotional outbursts prior to and after the implementation of the behavioral intervention technique.

In this scenario, the frequency for emotional outbursts was less after the implementation of the behavioral intervention technique. If a statistical difference is revealed, the amount of difference between the two frequencies would be considered unlikely to be due to chance, thus implying the behavioral intervention program was effective in reducing the frequency of emotional outburst among severely behaviorally challenged students with autism.

Remember, parametric tests are employed when the data are normally distributed, whereas non-parametric tests are employed when the data are skewed or non-normally distributed.

Normal Distribution:

Image Description: A bell-shaped normal distribution depicting +/- 1 to 3 standard deviations from the mean is presented.

Skewed or Non-Normal Distribution:

Image Description: A negative skew to the right and a positive skew to the left distributions are presented.

The Kolmogorov-Smirnov Test (> 50 samples) and the Shapiro-Wilk Test (< 50 samples) are tests used in SPSS to test for normality in the collected data.

Be sure to review this week's resources carefully. You are expected to apply the information from these resources when you prepare your assignments.

All resources for this week:

Book(s)

Green, S., & Salkind, N. (2017). Using SPSS for Windows and Mac analyzing and understanding the data (8th ed.). Boston, MA: Pearson.

Read Unit 10-39, 10-40, 10-41

Chi-square or chi-squared (x2). (2004). In D. Cramer & D. Howitt (Eds.), The SAGE dictionary of statistics (pp. 22-24). Thousand Oaks, CA: SAGE Publications Ltd.

doi: 10.4135/9780857020123

http://methods.sagepub.com.proxy1.ncu.edu/reference/the-sage-dictionary-of-statistics/n72.xml

Gao, X. (2012). Nonparametric statistics. In N. J. Salkind (Ed.), Encyclopedia of research design (pp. 915-920). Thousand Oaks, CA: SAGE Publications Ltd.

doi: 10.4135/9781412961288

http://methods.sagepub.com.proxy1.ncu.edu/reference/encyc-of-research-design/n272.xml

Thatcher Kantor, P., & Kershaw, S. (2012). Parametric statistics. In N. J. Salkind (Ed.), Encyclopedia of research design (pp. 1000-1003). Thousand Oaks, CA: SAGE Publications Ltd.

doi: 10.4135/9781412961288

http://methods.sagepub.com.proxy1.ncu.edu/reference/encyc-of-research-design/n303.xml

Video

Knapp, H. (Academic). (2017). An introduction to the chi-square test [Video file]. London: SAGE Publications Ltd.

http://methods.sagepub.com.proxy1.ncu.edu/video/an-introduction-to-the-chi-square-test-tuto

Document/Other

EDR-8201 SPSS Week 7 Worksheet

EDR-8201 Teacher Survey.sav Most of the SPSS activities in this course will use this SPSS data set. However, not every variable in the set will be used for each activity.
Teacher Survey.sav
Download Data File

Reporting statistics in APA style [Online document]. (n.d.). Northcentral University Commons.

https://vac.ncu.edu/sites/default/files/file_file/reportingstatsinapa_0.pdf

For This Assignment Below:

Analyze a Chi-Square Test

SPSS Week 7: Chi-Square

Attached are images from the teachersurvey.sav file that will help with assignment

Assume a researcher is interested in gathering information related to the distribution of teachers used in a research sample; or, if the surveyed teachers were evenly distributed across gender, across topic area, and gender across topic area.

Download the SPSS data set “teachersurvey.sav.” Not all of the variables in this SPSS file will be used for this assignment.

In this SPSS assignment, you will expand your understanding of inferential statistics involving a chi-square analysis.

• For each variable gender and topic, conduct a Chi Square analysis to test if there is an even distribution across each level of each variable. (Hint: For this test, use the Nonparametric Test under the Analyze tab.)
• Once this analysis has been completed, the researcher is interested in determining how the distribution appears across the two variables combined. Conduct a Chi Square goodness-of-fit test for cross tabulation of gender and topic area. (Hint: For this test, use the Descriptive => Crosstabs under the Analyze tab.)

• Upload the SPSS output.
• What are the null and alternative hypotheses for each variable?
• Report the results in APA format of the test for each of these hypotheses.

• Upload the SPSS output
• What are the null and alternative hypotheses for this test?
• Report the results in APA format of the test for each of these hypotheses.

3.Based on your personal experiences and interests, briefly discuss two variables to be used in a chi-square analysis.