Last bits of inferential statistics

Check in Proposal DRAFT due Tuesday Research in media assignment Tuesday Quiz Tuesday the 29 th –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 X 2 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 X 2 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