Analysis of Statistics Tests - Essay Example

Examples of parametric tests are t-tests and z tests which are used on both paired and independent quantitative data.

Nonparametric tests do not assume any particular distribution for the data; however, they look at the category or rank order of the values and ignore the absolute difference between them (Driscoll and Lecky 2001.). In addition to the application of these tests to quantitative data that are not normally distributed, nonparametric tests are also applied to nominal and ordinal data. According to Driscoll and Lecky (2001), examples of nonparametric tests include Chi-Square, Fisher exact test which is used for nominal data; and Wilcoxon, Mann-Whitney and Kolmogorov-Smirnov which are used for ordinal data.

Chi-Square (χ2) test is a very popular nonparametric test that is used on unpaired nominal data. This paper shows how the χ2 test is applied to data relating to gender and office locations of 60 sworn officers. The test is used to determine if there is a difference in the gender distribution among the three locations. According to Salkind (2009), the Chi-Square test is a very interesting test that allows the researcher to determine if what is observed in the distribution of frequencies represents what is expected to occur by chance.

Application of Chi-Square Test

The data relating to gender and office locations have been grouped in order to perform a Chi-Square test.  The test has more than one independent variable and so is described as a test of independence. The table below shows the arrangement of the data.

Gender Distribution Among Three Locations

Gender

Office 1

Office 2

Office 3

Total

Male

10

12

13

35

Female

8

5

12

25

Total

18

17

25

60

The table above shows that there are a total of 35 males and 25 females distributed across three locations. The test seeks to determine whether there are any differences in relation to the gender distribution across the three locations. Therefore, the null hypothesis (Ho) and research hypothesis would be stated as:

Ho: F1 = F2 = F3

According to Salkind (2009), the next step is to determine the level of risk or significance associated with the null hypothesis. As noted earlier the Chi-Square test is the appropriate statistic for this kind of data since it involves frequencies of mutually exclusive categories. The level of risk is normally set at p < 0.05.

The Chi-Square test (CHITEST) was used to calculate the compute the Chi-Square value and the CHIDIST function along with the degrees of freedom was used to compute the probability. The results in the table below which were calculated in excel show the results of the test.

Gender Distribution Among Three Locations

Office 1

Office 2

Office 3

Total

Gender

fo

fe

fo

fe

fo

fe

fo

fe

Male

10

11

12

10

13

15

35

35

Female

8

8

5

7

12

10

25

25

Total

18

18

17

17

25

25

60

60

Chi-Sq. by Group

0.81107

0.30541

0.52067

 χ2

1.63715

CHIDIST

0.65035

The CHIDIST value of 0.65 is less than the computed χ2 value and so the null hypothesis is rejected and so we conclude that the gender distribution is different in all three locations.