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QUESTION

 statistics    

Description
Complete the topic essay for this module. You may use Web resources, your textbook or any other resource. Answer the question fully; there is no minimum length for your answer (submittals are usually between 2 and 5 pages). The questions should be answered using MS Word and submitted as a MS Word document. Embed any pictures, tables, or data into the document.

Follow previous instructions for calculating Chi Square by hand, or using the spreadsheet.

For more details about how to manually calculate the chi-squared, view the brief video demonstration: https://www.youtube.com/watch?v=VskmMgXmkMQ

Instructions: Analyze the following table. Use the observed frequencies in the table to calculate chi square. Show your findings in a table with chi square (Chi square = 100.9 with 1 degree of freedom).

Link to SOC337 Mod13 Activity 1 Table. (http://ple.odu.edu/courses/202010/soc337/_assets_/document/module/013/soc337_mod13_selecting_statistics.pdf)

 

 SOC 337 – Selecting Statistics – Population Operational Definitions Race of Offenders

Type of Lawyer

White

Nonwhite

Total

Private

95

25

120

(47.5%)

(8.3%)

Court Appointed

105

275

380

(52.5%)

(91.7%)

Total

200

300

500

 

 

 

 

Subject Statistics Pages 6 Style APA

Answer

Calculate Chi Square

The Chi Square statistic is a non parametric statistical test commonly used for testing relationships between categorical variables.  The test is most commonly used to assess Tests of Independence when using a crosstabulation in a bivariate table (Adamu, Oguntunde, Okagbue & Agboola, 2018).  Crosstabulation presents the distributions of two categorical variables together, with the intersections of the categories of the variables appearing in the cells of the table.  The Test of Independence assesses whether an association exists between the two variables by comparing the observed pattern of responses in the cells to the pattern that would be expected if the variables were truly independent of each other (Adamu et al., 2018). 

Before conducting a chi square test the data must be checked to ensure that it meets the assumptions for the test. The variables should be categorical, such as nominal, dichotomous or ordinal, there should be independence of observation which means that a case can not occur in more than one group, the groups of the categorical variable must be mutually exclusive and in each group of the variable there must be at least five expected frequencies (Hopkins, Dettori, & Chapman, 2018).

In the table below are two variables namely “race of offender’ and “type of lawyer”. It shows expected values in each category.

The research question is as follows: is there a significant difference in the number of white and non white offender prosecuted between private and court appointed lawyers?

Or is the race of the offender prosecuted dependent on the type of lawyer?

 

 

Race of offender

Type of lawyer

White

Non white

total

Private

OBSERVED

95

25

120

EXPECTED

48

72

47

-47

47.50%

8.30%

24%

Court Appointed

OBSERVED

105

275

380

EXPECTED

152

228

-47

47

52.50%

91.70%

76%

Total

200

300

500

100%

100%

100%

 

The data shows that a person can fall in one of four categories:

  • White offender, private lawyer
  • White offender, court appointed lawyer
  • Non white offender, private lawyer
  • Non white offender, court appointed lawyer

In order to work out chi square the following formula is applied:

∑ [(O-E)2]E

Where:

O is the observed frequency

E is the expected frequency if everything were left to chance, i.e that the race of prosecuted offender was independent on the type of lawyer.

The table show the observed frequencies in each cell. In order to work out the expected frequency, the following formula is applied:

E = [row total*column total] /grand total.

To find the expected number of:

  • White offender, private lawyer,

[120*200]/500 = 48

  • White offender, court appointed lawyer

[380*200]/500 = 152

  • Non white offender, private lawyer

[120*300]/500 = 72

  • Non white offender, court appointed lawyer

[380*300]/500 =228

Chi square = ∑ [(O-E)2]E

(95-48)2/48 + (25-72)2/72 + (105-152)2/152 + (275-228)2/228

χ = 100.9

 

 

References

Adamu, P. I., Oguntunde, P. E., Okagbue, H. I., & Agboola, O. O. (2018). Statistical data analysis of cancer incidences in insurgency affected states in Nigeria. Data in brief18, 2029–2046. https://doi.org/10.1016/j.dib.2018.04.135

Hopkins, S., Dettori, J. R., & Chapman, J. R. (2018). Parametric and Nonparametric Tests in Spine Research: Why Do They Matter?. Global spine journal8(6), 652–654. https://doi.org/10.1177/2192568218782679

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