Analyzing Black Disparity Indices for Vehicle Stops in Police Municipalities in St. Louis County and

Data Collection

In that so much attention in the past two years has been devoted to Civil Rights, it seemed worthwhile to focus attention on black (African American) disparity indices for vehicle stops inside police municipalities across St. Louis County and City.Before going further, let’s make sure you understand what a Black Disparity Index actually is.The Ballwin Police Department can serve as an example. Below is the 2013 report from Ballwin; it is similar to what every police municipality must annually submit to the Missouri Governor.

The population of Ballwin is 23,735. Of that 23,735, 2.37% are black.  In other words, the proportion of blacks in this municipality is 2.37%. According to this report, the number of vehicle stops made in Ballwin during 2013 was 8982 and of that number 463 were black.  Therefore the proportion of stops that were of black drivers was 463/8962, or 5.15%. In order to find the disparity index one would do the following:

Clearly, if this number is greater than 1, proportionately more blacks than others are being stopped; if this number is less than one, proportionately fewer blacks than others are being stopped.  Ideally, in a perfect world, this number would be equal to 1, which would indicate that the number of blacks and whites within a municipality were being stopped in equal proportion to the number blacks and whites who live within the municipality. (Note: due to random chance anything “very close” to 1 is good. With “very close” depending on the sample sizes)

In order to begin the analysis of black vehicular stops, the first thing one should do is to create a random sample of police municipalities from the population of police municipalities in St. Louis City and County. (See a listing on page 5 of this paper; however, you will be provided with a listing inside an Excel document, which can be found inside this same Descriptive Statistics Project folder.)A random sample of 20 should be sufficient in this particular case.Let’s not include Ferguson as one of the selected municipalities. In the end it would be interesting to compare Ferguson to the descriptive data collected for your sample.  

In order to generate a sample of 20 randomly selected municipalities, all 58 municipalities (not including Ferguson) must have had an equal chance of being selected for that study. Excel will aid in selecting those 20 randomly selected municipalities that will make up your sample. Below these instructions you will find a tutorial regarding how one goes about selecting a random sample of 20 police municipalities from the list of 58 given municipalities.  

Tables and Charts

After you have created your random sample, please list the municipalities that comprise your random sample along with their individual black disparity indices inside the Excel document that has been provided for you. You can remove those you do not use; however, don’t remove Ferguson.

The basic idea of this project is for you to analyze the black disparity indices of these 20 municipalities using the techniques you have learned in Chapters 2 and 3 of our textbook.  Based upon your random sample, you are to describe these data in a manner that people who read your description can understand what is happening in St. Louis County in terms of black disparity indices.  (Remember that if a sample is indeed a random sample, then it should be representative of the entire population.)

Your project should consist of the following items.It should be typed inside a Microsoft Word document with appropriate statistical symbols and expressions. (Go back and look at how you should be writing mathematics inside Microsoft Word. This is why we practiced typing mathematical expressions using the Microsoft Equation editor.) You will be doing some parts of this assignment inside Excel; however, you must copy and paste those Excel parts into your Word document at the appropriate places inside the Word document. Please include the items in your paper in the order specified here.

1. Include a listing of your data with a complete description of how the data were obtained and what these data represent.  Be really specific because your reader needs to understand how the data were collected for this project.Be sure to copy and paste your table of black disparity indices from Excel for your 20 municipalities into your Word document; so your reader can see the index for each municipality comprising your sample.

2. Include the following tables and charts. Make sure each table includes a meaningfultitle (not something like “Frequency Table”) and that each of your columns is labeled. Make sure each chart/graph includes a meaningfultitle and that your horizontal and vertical axes have titles as well. You can copy and paste the tables and charts from Excel into your Word document.  

-Frequency Table

-Relative Frequency Table

-Cumulative Frequency Table

-Histogram

-Relative Frequency Histogram

3. By using Excel’s expertise, calculate the following statistics which will describe the central tendency in your sample. Be sure to clearly label each value.

Central Tendency

-Mean

-Median

-Mode (if any)

-Midrange

Compare and contrast these measures of central tendency.  Can you tell from your different central tendency values and also by looking at your histogram as to whether the sample represents a normal distribution? Or…is it possibly skewed to the left or to the right? Discuss this for the reader.

4. Calculate the following statistics which will help show how variableyour data are. Do these calculations by using Excel.

-Range

-Standard Deviation

-Use the Empirical Rule show your reader the two values between which, theoretically, roughly the middle 68% of the data should fall. Be sure to explain to your reader how this was determined.

-Again using the Empirical Rule, show your reader the two values between which, theoretically, roughly the middle 95% of the data should fall.  

Now look back at your data – does it look as if these theoretical values hold true? Discuss this.

5. Find the z-score of your highest and lowest data elements?  

-For each of the z scores you are calculating, show the formula you are using, the values you substituted into the formula and the z score that was calculated. Look back at your first assignment in this class (Typing Mathematics using Word) – you will see an example of exactly how this should look.

-Discuss what these z-scores are telling you.  Remember that these data values represent black disparity indices for specific municipalities. What do these z scores tell you about the highest and lowest black disparity values in your sample?

-What is the z-score of the mean of your data?  Explain why it should be that value?  

6. Let’s look at another way to describe your data.

-Find the values that are considered to be included in the 5-number summary of your sample.  

-Construct a Box and Whiskers Plot for your sample.  Explain does this Box and Whiskers Graph is telling you? (Information regarding how to do this can be found in the last section of Chapter 3 or check out the FAQ Section of our course.)

7. Based upon all you have calculated and graphed, what might be an overall conclusion regarding the description of your sample of 20 municipalities?  You might want to address these items.

-Discuss your findings – what have you been able to determine?

Variability

-How would you describe your data to someone else? Is it normally distributed?

-What did the central tendency scores tell you?

-How variable was your data?

-What municipalities did not quite seem to follow along with what would normally be expected?

-Can your sample’s results be logically extrapolated to the entire St. Louis County and city area from which it was drawn?

-How does Ferguson compare with your summary statistics? Is it in line with the rest of the county based upon the results from your sample? Would it have been considered to be an unusual value when compared with the rest of your data?

Include in your overall conclusion your thoughts on how analyzing these data have helped you shed light onto a social issue such as this.

Descriptive Statistics Project

In order to create a random sample, it is necessary to use the RANDBETWEEN function inside Excel.  To do this, we first have to make sure that the Analysis Toolpaks are clicked on.  Here are the instructions about how to do this.

In Excel 2010,  2013, 2016, and 365, go to the File menu and select Options from the menu.  Click on Add-Ins on the left-hand side.  Then go to the bottom of that page where it says Manage Excel Add-Ins and click Go.  Finally, you will see a little dialog box, in which you must click on the first two items.  Click Okay and we are ready.

In Excel 2007, go to the Office button (at top left).  Click on the Excel options at the bottom on that page.  Click on Add-Ins on the left hand side of the new page. Then go to the bottom of that page where it says Manage Excel Add-Ins and click Go.  Finally, you will see a little dialog box, in which you must click on the first two items.  Click Okay and we are ready.

Now we are ready to create a list of 20 random numbers between 2 and 59.  (Notice that the police municipalities are listed in A2 through A59.  So if one of our random numbers is 13, we would use the Charlack Park Police Department (the police municipality in row 13) as a member of our sample.)

Click inside cell C1 in Excel.  Once there, type this in:  =RANDBETWEEN(2,59)

Then press Enter.  You will notice there is a number now inside C1 that is between 2 and 59, inclusive.  Go back and click on cell C1 again and move your mouse until you can see the little plus sign at the lower right-hand corner of that cell.  (In other words, I am trying to get you to find the fill handle – if this is not clear to you, see the Excel tutorial inside the Preliminary Tasks folder under the Course Materials tab.)  Pull the fill handle down until you have 20 random numbers inside cells C1 through C20.  Once you have them, you will have to do something in order to keep them from changing once you do anything else inside Excel.  (Excel has a terrible habit of regenerating those numbers over and over again.)  Here is what you do:

Copy (as in copy and paste) the numbers inside cells C1 through C20.  Then go to the Paste button at the top left of the ribbon under the Home menu, and click on the down arrow there.  Select Paste Values and then say Okay.  What that does is to paste the 20 different values you have generated; it does not paste the RANDBETWEEN function that was used to gather them; thus they will not change.

Check your list to see if there are any duplicates.  If there are, you will need to click into the cell of the duplicate and then type in:  =RANDBETWEEN(2,59)  That will succeed in regenerating another random number.  If it is not a duplicate, then copy and paste it as a value just as you did above.  Keep doing this until your list of 20 numbers does not contain any duplicates at all.

Now, look back at the listing of the 58 police municipalities.  Select the municipalities whose numbers are in your list of randomly generated numbers; then you will have made a listing of the 20 municipalities that will compose your random sample of police municipalities. In the end I would like to see your listing of the 20 municipalities that make up your sample.  Please list the municipality as well as the Black Disparity Index for that municipality.  

In order to remove a column inside Excel, all you have to do is to place your cursor on the letter associated with that column at the top of the screen. (The cursor becomes a down arrow.)  Click once and then right click and select Delete. To remove a row inside Excel, all you have to do is to place your cursor on the number associated with that row on the left of the screen. (The cursor becomes a right arrow.)   Click once and then right click and select Delete.)