Question

Assumptions guides (be sure to explain how your data meets these assumptions and perform the applicable tests.

Applicable Tests: T-tests /Chi-Square / Correlation / Regression / ANOVA / Mann-Whitney U / Wilcoxon Signed Rank / Kruskal-Wallis

Create a document explaining the data you have decided to use and what statistical test you intend to use. Be sure to use the decision tree provided in this activity. Analyze your data to insure that it meets the assumptions of the test (for example parametric vs. non-parametric). Please Evaluate and Utilize These police shooting death totals.

shot to death by the police 2017-18
RACE	2017	2018	2017 MALE	2018 MALE
WHITE	457	211
BLACK	223	102
HISPANIC	179	68
OTHER	44	18
UNKNOWN	84	120
TOTAL	987	519	940	492

Answer 1

For shot to death by the police data in 2017 and 2018. Here we may be interseted in finding out whether the data values obtained for year 2017 is associated with year 2018. The Chi-square test of independence is formed to test the association between two year data.

The Chi-square statistic is a non-parametric test which takes the assumption that,

1) the distribution of the data is not known (i.e. non-parametric),

2) The data values are measured at no nominal or ordinal level (nominal in this case) and

3) The sample sizes of the groups that studied are unequal.

The Chi-Square test of independence is used to determine if there is a significant relationship between two factors (RACE and YEAR). The Chi-Square test of independence is performed in following steps,

Step 1: The hypothesis is defined as,

Null hypothesis: There is no association between two variables.

Alternative hypothesis: There is an association present between the two variables.

Step 2: The significance level for the test is,

Step 3: The Chi-Square test statistic is obtained as follow,

The observed values are,

Observed Values
RACE	2017	2018	TOTAL
WHITE	457	211	668
BLACK	223	102	325
HISPANIC	179	68	247
OTHER	44	18	62
UNKNOWN	84	120	204
TOTAL	987	519	1506

The expected values are obtained using the formula,

The expected values are,

Observed Values
RACE	2017	2018	TOTAL
WHITE	437.79	230.21	668
BLACK	213	112	325
HISPANIC	161.88	85.12	247
OTHER	40.63	21.37	62
UNKNOWN	133.7	70.3	204
TOTAL	987	519	1506

Now the Chi-Square Value is obtained using the formula,

Step 4: The P-value for Chi-Square statistic is obtained using the chi square distribution table,

Step 5:

The null hypothesis is rejected. It can be stated now, the two variables are dependent. There is a statistically significant association between two variables Race and year.

Similarly, the test is performed for the two variable, Gender (Male, Female) and Year (2017 and 2018).

From the data values provided,

GENDER	2017 MALE	2018 MALE
MALE	940	492
FEMALE	47	27
TOTAL	987	519

The Chi-Square test of independence is performed in following steps,

Step 1: The hypothesis is defined as,

Null hypothesis: There is no association between two variables.

Alternative hypothesis: There is an association present between the two variables.

Step 2: The significance level for the test is,

Step 3: The Chi-Square test statistic is obtained as follow,

The observed values are,

Observed Values
GENDER	2017 MALE	2018 MALE	TOTAL
MALE	940	492	1432
FEMALE	47	27	74
TOTAL	987	519	1506

The expected values are,

Expected Values
GENDER	2017 MALE	2018 MALE	TOTAL
MALE	938.5	493.5	1432
FEMALE	48.5	25.5	74
TOTAL	987	519	1506

Now the Chi-Square Value is obtained using the formula,

Step 4: The P-value for Chi-Square statistic is obtained using the chi square distribution table,

Step 5:

The null hypothesis is failed rejected. It can be stated now, the two variables are independent. There is a no significant association between two variables Gender and year.