Statistics Chapter 1 Statistical Reasoning: Investigating a Claim of Discrimination

1. Section 1.2 Continued Discrimination in the Workplace: Inference through Simulation: Discussion StatisticsChapter 1 Statistical Reasoning:Investigating a Claim of Discrimination

2. Practice 5 – a complete answer • Average age 48.6 • Ten workers were selected from 14, so to simulate this we would: • List the 14 ages and assign numbers 1-14. • Select 10 different employees randomly from the group using random integers. • Find the average of these 10 ages. • Repeat these steps many times. • Create a dot plot of the averages. • This can then be used to calculate the proportion or probability of randomly selecting 10 employees of an average age within a certain range.

3. Practice 5 cont. • The average was 48.6. 45 of 200 dots are above 48.6 for a proportion of 0.225. • Meaning that the probability of getting an average age of 48.6 or higher in a single trial is 22.5%. • This evidence would not help support Mr. Martin’s case. It would mean we would expect this to happen by chance 22.5% of the time, which is a reasonable chance and not a rare occurence.

4. Dot Plot from 1.2 Simulation • Approximate dot plot: • Explain why we consider looking at the probability (proportion) of a range of values instead of a specific value. • Each individual value may or may not even appear, so it is difficult to estimate a probability at a specific value.

5. 1.2 Simulation Reporting • Create a classroom Dot Plot of your averages for each repetition. • Look at the Dot Plot: How many times did we get a result of 58 or higher? • Based on our simulation, what is the probability that you would randomly get an average age of 58 or higher? • Probability: proportion of successes out of total trials in the long run. • If Westvaco was truly unbiased by age would you expect that they chose the people they did? Explain.

6. 1.2 Simulation Discussion • If we decided that the probability was high enough that there was reasonable possibility that Westvaco could have chosen those employees without bias, then they may be off the hook. • However, if the probability was very low, we can say that it is very unlikely that they chose those employees unbiased of age. • They may still have valid reasoning, but now the need for an explanation is on them.

7. Simulation/Dot plot Inference • Our overall probability of getting a 3 person average age of 58 or older for the day was about 2-6%. What does this mean to us? • If we truly selected 3 employees by some other means that did not have anything to do with age, the average age would be 58 or higher approx. 4% of the time. • In one round of layoffs, there is a 3-6% chance of having an average age of 58 or higher. • Is that significant enough to support Mr. Martin’s case for age discrimination? • Note: It is typical for a court to require 0.025 or 2.5% or less for it to be considered truly significant enough to reject that it happened by chance.

8. Summary Tables • What is some key information you can get from summary tables? • Actual counts of certain characteristics within cases. • Maybe most importantly, the proportions of characteristics within cases.

9. Context and Type of Data • Consider the following information: • The number of violent crimes in a particular city has risen over the past 10 years; in 1995 the police documented 437 violent crimes, whereas in 2005 there were a total of 541 documented violent crimes. • Is this data sufficient to draw a reasonable conclusion regarding the level of change in violent crime? Explain • Not really…we don’t know the change in the population of the city. • If we did, a proportion of violent crime to population would be useful.

10. 1.2b Homework • Page 17 P4 • Page 18 E9, E12, E13 • On E9 you may use a Calculator simulation instead of slips of paper. • Be sure to answer questions completely with the context of the situation as the focus.