The Role of Statistics Sexual Discrimination Problem A large company had to downsize and fire 10...

The Role of Statistics

Sexual Discrimination Problem A large company had to downsize and fire 10 employees. Of these 10 employees, 5 were women. However, only 1/3 of the company’s employees were women. This discrepancy has led the women who were fired to file a sexual discrimination lawsuit.

Do they have a legitimate claim?


What are the two possibilities in this case? they have a legitimate claim:

the company fired a higher proportion of women on purpose

they don’t have a legitimate claim:

this could have occurred by random chance


Which of the two possibilities can we actually assess? not the first one

we cannot know what the boss was thinking however, we can estimate the probability of getting a

result as surprising as this by random chance


Simulate the firing by using a population of beads to

represent the population of the company

white = women

black = men

Draw 10 beads at random and count the number of

women fired (# of white beads).


Collect class data and estimate the probability of having 5

or more women fired by random chance

(company is telling the truth).


Does this give evidence of discrimination (the women

were fired on purpose)?

NO! Since it is somewhat likely to get 5 or more

women by random chance alone, we do not have

evidence that women were discriminated against.


Summary:

Based on the makeup of the company, we would expect to

have 3 or 4 women fired. However, firing 5 or more

women could have occurred by random chance so we

should not decide the company is guilty.

How many women fired would make you suspicious?

In statistics, it is always possible that we make the wrong

decision. More on this later…


STATISTICS is the science of collecting, analyzing, and

drawing conclusions from data. Statistics is also the art of

distilling meaning from data.

The POPULATION OF INTEREST is the entire

collection of individuals or objects about which

information is desired.


When you study an entire population, it is called a

CENSUS.

A SAMPLE is a subset of the population, selected for

study in some prescribed manner.


DESCRIPTIVE statistics is the branch of statistics that studies methods for summarizing data.

INFERENTIAL statistics is the branch of statistics which involves generalizing about a population based on information from a sample of that population.

Statistical INFERENCE is the process of drawing these generalizations.


A VARIABLE is any characteristic whose value may

change from one individual to another.

Ex:

DATA results from making observations on one or more

variables. It is important to remember that a set of

information is not data unless it comes in a context.


A DISTRIBUTION shows the values a variable can take and how often it takes those values.

Ex:


A UNIVARIATE data set consists of observations on a

single variable.

Ex:

A BIVARIATE data set consists of observations of two

variables for each member of the sample.

Ex:


A variable is CATEGORICAL (or qualitative) if the

possible responses fall into categories.

Ex:

A variable is NUMERICAL (or quantitative) if the

possible responses are numerical in nature.

Ex:


Quantitative variables usually include units, which tell

how the variable was measured. For example, if you are

told the weight of an animal is 12, you wouldn’t know

very much until you were informed of the unit

(e.g. tons or milligrams).


Observations of categorical data are usually recorded with

words (e.g. Honda, brown), but can also be recorded with

numbers. Area codes are an example. Living in the 626

area code isn’t necessarily better than living in the 310

area code, even though it is higher numerically. In cases

like these, the numbers are just labels for different

categories.


Many variables can be used as a categorical variable or a

quantitative variable. For example, scores on the STAR

test are recorded numerically, but also placed into

categories such as “proficient” and “basic”.


Numerical data is DISCRETE if the possible values areisolated points on the number line.Ex:

Numerical data is CONTINUOUS if the possible valuesform an entire interval on the number line.Ex:

In general, you MEASURE continuous variables and COUNT discrete variables.


For each of the following variables, determine if they

are categorical or numerical. If it is numerical,

determine if it is continuous or discrete: length of a pen type of pen number of pens in a box




determine if it is continuous or discrete: color of pants number of pockets length of inseam




determine if it is continuous or discrete: subject of book number of pages area of a page

The Role of Statistics Sexual Discrimination Problem A large company had to downsize and fire 10...

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