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?

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