Chi-Square

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Mathematics

Description

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.

Unformatted Attachment Preview

SPSS Statistics Untitled 7 [DataSet 10) - IBM SPSS Statistics Data Editor A e 1 Identifie Gender Experien Age Topic ClassSiz Score On Score Tw ProdOne Conflict *** var var BER var var var се e e 0 1 52 25 1 1 18 64 95 1 25 Competitive 2 1 35 14 1 23 68 87 2 28 Competitive 3 2 45 10 3 27 3 74 79 36 Cooperative 4 1 47 20 2 21 75 4 78 38 Competitive 5 2 62 30 5 21 76 85 34 Competitive 6 2 29 2 29 6 79 96 36 Cooperative 7 7 2. 50 23 4 25 80 90 40 Cooperative 8 N 43 13 3 31 82 92 41 Cooperative 9 9 1 54 29 2 24 68 86 22 Competitive 10 10 1 40 19 2 25 70 74 38 Cooperative 11 11 2 44 22 2 32 74 79 39 Cooperative 12 12 2 S3 5 1 30 76 85 34 Competitive 13 13 2 56 16 1 19 78 81 38 Cooperative 14 14 2 28 11 2 28 79 83 37 Competive 15 15 1 51 15 2 21 82 96 45 Cooperative 16 16 1 30 2 4 22 85 84 46 Cooperative 17 17 2 45 15 3 27 71 75 30 Competitive 18 18 1 36 11 1 29 73 89 34 Competitive 19 19 2 57 18 2 30 75 93 33 Competitive 20 20 1 58 10 2. 20 77 77 36 Competitive 21 21 1 59 21 3 27 78 76 38 Cooperative 22 22 1 34 Сл 2 23 80 87 42 Cooperative 23 23 2 48 18 2. 33 83 84 46 Cooperative 24 24 2 50 21 1 19 86 92 49 Cooperative 25 25 1 57 17 4 15 73 99 37 Competitive 26 26 2. 48 15 4 21 74 83 38 Cooperative 27 27 1 39 18 2 24 77 84 32 Competitive Data View Variable View Untitled7 [DataSet 10] - IBM SPSS Statistics Data Editor AN IBM SPSS Statistics Processor is rea W HH FR NO esc 2013 888 F4 FS F7 FO % 5 2% lê l 3 W R Y S 기 Z /*/ . I B M comunand 0 Measure Columns Role Align Label Values Width Missing Name Decimals Type Nominal Input None 8 Right None 1 Identifier Numeric 0 8 Nominal Input 8 Right None 1=male, 2=fe... None 2 Gender Numeric 8 0 8 Scale Right Input None None 3 0 8 Age Numeric 8 Scale Right Input None None Experience Numeric 8 0 None Nominal 8 Right Input 1=math,2=SCİ... None 5 Topic Numeric 8 None 8 None Right Scale Input 6 ClassSize Numeric 0 8 None 8 Right Scale None Input 7 Score One Numeric 0 8 None 8 None Right Scale Score Two Input Numeric 8 0 清 None None 8 Right Scale Input Numeric 9 0 ProdOne 8 None Left 8 Nominal 10 None Conflict 0 Input String 11 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Data View Varble View IBM SPSS Statistics Processor is read 6 m a W UNI Huu! JEO PEO F7 EVO * tot W R Y u SIZE:1:1:13 LA Tera el S I Z х C V go alon SPSS Statistics File Edit View Data Transform Transform Analyze Graphs Analyze Graphs Utilities Extensions Window Help LE Teacher Survey (2).sav [DataSet 1] - IBM SPSS Statistics Data Editor AL 14 H var var ScoreOn ProdOne ca Conflict Score Tw ClassSiz var var Identifie Topic Experien LA Gender Age e 0 e ce 37 Competitive 15 73 99 17 25 57 1 25 38 Cooperative 74 83 21 15 4 26 2 48 26 77 84 32 Competitive 24 18 2. 27 39 1 27 77 76 35 Competitive 26 1 28 12 1 1 36 28 78 75 36 Competitive 23 8 3 29 29 N 29 72 45 Cooperative 3 24 81 3 30 52 1 30 84 88 49 Cooperative 28 31 68 33 2 N 31 87 48 Cooperative 87 25 32 2 45 16 3 32 84 26 77 36 Competitive 33 2 4 56 29 N 33 71 33 Competitive 83 34 1 20 40 19 1 34 2 94 34 Competitive 35 33 23 75 1 A 35 36 Competitive 36 2 47 17 27 76 87 2 36 58 38 Cooperative 30 25 79 1 37 3 79 37 38 49 48 Cooperative 1 20 4 27 76 83 38 39 2 39 48 Cooperative 11 30 79 1 89 39 40 2 42 14 4 22 91 49 Cooperative 94 40 41 42 43 . 44 45 46 47 48 49 50 51 Data View Variable View IBM SPSS Statistics Pro JUN 70 5 5 ELI a PW TA JPEG esc * 20 F3 F7 $ 2 # 3 % 5 & 7 tab W R Y S I J K Z C с V M ge option command
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Explanation & Answer

buddy...i had hard time understanding data given by you. I am sending solution. However, if possible, send data in excel so thatI recheck question.regardds

CHI-SQUARE ANALYSIS (VARIABLE: GENDER, TOPIC)

Frequencies

1=male, 2=female
Observed N

Expected N

Residual

1

18

20.0

-2.0

2

22

20.0

2.0

Total

40

1=math,2=science,3=art,4=foreign language
Observed N

Expected N

Residual

1

10

10.0

.0

2

14

10.0

4.0

3

9

10.0

-1.0

4

7

10.0

-3.0

Total

40
Test Statistics
1=math,2=scien
ce,3=art,4=fore
ign language

1=male,
2=female
Chi-Square
df
Asymp. Sig.

.400a

2.600b

1

3

.527

.457

a. 0 cells (0.0%) are shown to have expected
frequencies less than 5. The minimum expected
cell frequency ...


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