Assessing Hypotheses: Means & Graphs

Lecture plan Hypotheses Cross-tabs, means, or graphs? Comparing means Creating and interpreting graphs

Hypotheses What are hypotheses? –Testable statements about empirical relationships –Derived from theory. Examples: –The more religious are more Republican. –Democratic states do not go to war with one another. –Droughts depress the vote of the Democratic party. How do we test hypotheses? –It depends on the data.

Continuous DV Crosstabs works for nominal and ordinal dependent and independent variables But what do we do when the dependent variable is interval and the independent variable is nominal? –Compare means; Bar chart (more on this later). What do you do when the dv is interval and the iv is ordinal? –Line graph (more on this later). When both are interval?

Continuous v. Nominal Let’s start with a question that has puzzled social scientists for centuries: “Do Canadians have more fun than Brits and Americans?” So we hypothesize: “Canadians will report higher levels of fun than Brits and Americans.” Validity problems?

Do Canadians Have More Fun? Fortunately, you have a “thermometer” measuring the self-reported fun experienced by Canadians, Brits, and Americans (technically called the Fun-O-Meter). What is your (continuous) DV? What is your (nominal) IV? How would you test the hypothesis that Canadians have more fun than Brits or Americans?

Comparing Means Right-O! Compare the mean of the dependent variable across values of the independent variable. This is how you do it…

Comparing Means Who has more fun? NationalityMeanNStd. Deviation Canadians British Americans Total

Graphical Comp of Means: Bar Chart Continuous v. categorical (nom, ord) This is not a frequency bar chart! TV hours per week

How’d that happen? Graphs  Bar Simple Summaries Define

Bye Bye Nominal; Hello Line Graphs Works for all levels of measurement except nominal data –Continuous v. nominal (ordinal): Complements means comparison. –Ordinal v. Ordinal (numerically coded) –Continuous v. Continuous Let’s look at ourselves again: –Two ordinal variables: –7-category Dem Party L-R Placement Variable –5-category Religious Attendance Variable Do more religiously observant students view the Dem Party differently than less observant students?

Line Graph: Dem L-R v. Religious “Negative Relationship”

Line Graph: Rep L-R v. Religious “positive” or “curvilinear”

How’d that happen? Graphs  lines… Simple Summaries for groups of cases Define Next: Other summary function Enter variables OK

Continuous v. Continuous? Hmm… what if BOTH the dependent and independent variables are continuous? DV: Hours spent exercising and playing sports. IV: Hours spent watching TV. What would happen if we just line graphed “TV” against “exercise”???

Hmm…

This rolling average takes the mean of the original observation and those two hours before and after.

Or, we can categorize one of the variables.