Last bits of inferential statistics

Check in

• Proposal DRAFT due Tuesday

• Research in media assignment Tuesday

• Quiz Tuesday the 29th

– Will cover statistics material– Multiple choice

Conducting statistical tests

• Testing our hypotheses numerically

• Do the data support the null distribution?

• Do the data support the alternate distribution?

• Tests tell us if the difference in distributions is significantly different– Not just look different, but different enough so

we are pretty sure its not an accident

Some basic tests

• Remember there are many different types of distributions

• The normal distribution and others

• Tests are often named for their distributions

Tests—first look

• Chi-Squared– The X2 distribution

• T-test– The students T distribution

• Rho– The correlation coefficient R– Assumes a normal distribution or T

distribution

How to choose which test?

• Many tests may answer the same type of question

• Which test you use depends on your questions and variables

• Are your variables continuous or categorical?

• May also matter if independent variable is one type, and dependent variable is another type

What type of variable do I have

• Independent variable– The predictor– E.g. If I believe that gender predicts income,

then gender is the IV

• Dependent variable– The outcome– E.g. if I believe that anxiety predicts eating

habits, then eating habits is the DV

What type of variable do I have?

• Not all questions have an independent and dependent variable

• If I’m asking if two things are ASSOCIATED or CORRELATED there is no actual IV or DV

• A variable may be an IV in one question and a DV in another question, and vice versa

• It depends on my question

Continuous vs. categorical?

• Continuous– May actually be based on ordinal– When I have a large range of numerical

ratings– Height, weight– Symptoms, feelings

Continuous vs. categorical

• Categorical– May have levels– Has few categories– 1,2,3– Yes/no– Red/blue

Which test?

• If my question is– Are these two groups different?

• And my outcome is – Categorical

• I use a X2 test

Differences between 2 groups

• IV is 2 groups– E.g. men and women– Catholics and Protestants– People who have a peanut allergy and people

who don’t

• So I know that the IV is categorical

Differences between 2 groups

• If DV is also categorical

• Will also be a sort of “grouped” variable– Employed/unemployed– Married/not married– College degree/no college degree

Chi Squared Test

• If our predictor is categorical

• And our outcome is categorical

• Then we use a chi-squared test– A “2 x 2 table approach”

Example

• Does gender predict employment– Gender is categorical– Employment is categorical– This is a chi-squared test

• Tells us if there is a difference in the expected rate of occurrence, and the observed rate of occurrence

Example

• Assume gender is 50/50• If gender does NOT predict employment,

then we expect equal numbers of men and women to be employed

• If gender DOES predict employment we observe unequal numbers of men and women employed

• Chi square tests if observed and expected are significantly different

Which test?

• If my question is are these 2 groups different

• And my outcome is continuous

• I use a T-test

T-tests

• Also a test of difference between groups

• When the IV is categorical

• And the DV is continuous

• E.g. IV—men/women

• DV—height in inches

T-tests-examples

• IV—Dogs/Cats

• DV—weight in pounds and ounces

• IV—employed/unemployed

• DV—income in dollars

• IV—full time student/not full time

• DV—average hours of sleep per night

Which test?

• If my question is are these characteristics related or unrelated

• I am looking at the relation between two continuous variables

• I use a correlation test

Correlation

• Not a test of differences between groups

• A test of whether two continuous variables are related or unrelated

• The statistic is R

Examples

• Height and Weight

• Grade point average and hours of study

• Hours of sleep and scale measure of exhaustion