Find the expected values for the Find the expected values for the following contingency table:following contingency table:

A study examined whether the risk of hepatitis C was A study examined whether the risk of hepatitis C was related to whether people had tattoos and to where related to whether people had tattoos and to where they got their tattoos. they got their tattoos.

Warm-Up 2/23/11Warm-Up 2/23/11

Hepatitis C No Hepatitis C

Tattoo, parlor 17 35Tattoo, elsewhere

8 53

None 22 591

{{

Making Sense of Making Sense of Statistics!!!!Statistics!!!!

Which tests work and why…

What were the expected What were the expected values???values???

Let’s Look at the Warm-UpLet’s Look at the Warm-Up

Hepatitis C No Hepatitis C

Tattoo, parlor 3.90 48.1

Tattoo, elsewhere

4.58 56.4

None 38.5 474.

When doing a chi-squared test of When doing a chi-squared test of

independence you independence you CANNOTCANNOT have have

an expected value an expected value < 5< 5

We have a problem!!!We have a problem!!!

How could we change the How could we change the contigency table to make contigency table to make

this problemthis problem

Hepatitis C No Hepatitis C

Tattoo, parlor 3.90 48.1

Tattoo, elsewhere

4.58 56.4

None 38.5 474.

DISAPPEAR

How?How?

Combine categories…Combine categories…

Which ones???Which ones???

Combine “Tattoo, parlor” and Combine “Tattoo, parlor” and

“Tattoo, elsewhere” to create a “Tattoo, elsewhere” to create a

category “TATTOOS”category “TATTOOS”

Need to increase observed Need to increase observed values…values…

  Hepatitis C No Hepatitis C

Tattoo 25 88

None 22 491

New Contingency TableNew Contingency Table

  Hepatitis C No Hepatitis C

Tattoo 8.48 105None 38.5 474

Are the expected values all >5?Are the expected values all >5?

Both linear regression and chi-squared Both linear regression and chi-squared test of independence are trying to show test of independence are trying to show if there is a relationship between two if there is a relationship between two variables…so what do we need to look variables…so what do we need to look at to decide?at to decide?

The TYPE of data: The TYPE of data: CATEGORICAL – use chi-squared testCATEGORICAL – use chi-squared test QUANTITATIVE – use linear regressionQUANTITATIVE – use linear regression

But what if I am not told But what if I am not told what test to use???what test to use???

Need to be able to make a contingency Need to be able to make a contingency tabletable Need categories for each variable in order Need categories for each variable in order

to create a contingency tableto create a contingency table

When collecting data to use a When collecting data to use a χχ2 2 - - test on, test on, you need to be able to tallyyou need to be able to tally Ex: Dominant Hand vs. Walked Left/RightEx: Dominant Hand vs. Walked Left/Right

Cannot have expected value < 5Cannot have expected value < 5

ΧΧ22 – Test: Categorical Data – Test: Categorical Data

Need to have variables to put on x-axis and Need to have variables to put on x-axis and the y-axisthe y-axis

For linear regression to be useful in For linear regression to be useful in determining the relationship between two determining the relationship between two variables the scatterplot must be “straight variables the scatterplot must be “straight enough”enough”

No outliers No outliers

Linear Regression: Linear Regression: Quantitative DataQuantitative Data

Even if you hit the fast food joints for Even if you hit the fast food joints for lunch, you should have a good breakfast. lunch, you should have a good breakfast.

Nutritionists, concerned about “empty Nutritionists, concerned about “empty calories” in breakfast cereals, recorded calories” in breakfast cereals, recorded facts about 77 cereals, including their facts about 77 cereals, including their Calories Calories per serving and per serving and SugarSugar content content (in grams). How are calories and sugar (in grams). How are calories and sugar content related in breakfast cereals?content related in breakfast cereals?

Which Statistical Test???Which Statistical Test???

Company policy calls for parking spaces Company policy calls for parking spaces to be assigned to everyone at random, to be assigned to everyone at random,

but you suspect that may not be so. but you suspect that may not be so. There are three lots of equal size: lot A, There are three lots of equal size: lot A, next to the building; lot B, a bit farther next to the building; lot B, a bit farther

away; and lot C, on the other side of the away; and lot C, on the other side of the highway. You gather data about highway. You gather data about

employees at middle management level employees at middle management level and above to see how many were and above to see how many were

assigned parking in each lot.assigned parking in each lot.

Which Statistical Test???Which Statistical Test???

There is some concern that if a woman There is some concern that if a woman has an epidural to reduce pain during has an epidural to reduce pain during

childbirth the drug can get into the childbirth the drug can get into the baby’s bloodstream, making the baby baby’s bloodstream, making the baby

sleepier and less willing to nurse. In 2006 sleepier and less willing to nurse. In 2006 a study was conducted at Sydney a study was conducted at Sydney

University. Researchers followed up on University. Researchers followed up on 1178 births, noting whether the mother 1178 births, noting whether the mother had an epidural and whether the baby had an epidural and whether the baby

was still nursing after 6 months.was still nursing after 6 months.

Which Statistical Test???Which Statistical Test???

Colleges use SAT scores in admissions Colleges use SAT scores in admissions process because they believe these process because they believe these

scores provide some insight into how a scores provide some insight into how a high school student will perform at a high school student will perform at a

college level. Data was collected on SAT college level. Data was collected on SAT scores and freshman year GPA to test scores and freshman year GPA to test

this belief.this belief.

Which Statistical Test???Which Statistical Test???

Get in to pairs and come up with data Get in to pairs and come up with data you could collect and research questions you could collect and research questions you could answer using:you could answer using:

Linear RegressionLinear Regression

Chi-Squared Test of IndependenceChi-Squared Test of Independence

Group Work