Week 9/10 - Inferential Stats

Tests of relationships

Tests that examine relations/associations among variables

• Chi-Square test

• Correlation

• Regression

Chi-Square

Use to examine whether systematic association exists between two variables (nominal)

ex. Are men heavy drinkers of beer or is that js coincidence

Compute cell frequencies based on no association and compare frequencies

See slide abt the Frequency equations

Computing the Chi-Sq

See slide abt the Frequency equations

Limitations of Chi-Square tests

• Can only tell us is a relationship exists

  • Cannot tell us is:

    • The relationship is pos or neg

    • The strength of the relationship

  • Why

  • Cannot use if cells have less than 5 observations

• If we have interval or ratio data

  • we have more info

  • Use correlation/regession

    • Direction and strength of relation

Correlation and Regression

Is there a relationship between any two variables

• Are the effects significant

• How big/small is the effect

• Including dummy variables and interpreting them

Correlation

Strength of linear relationship between two variables X and Y

• Correlation coefficient ( r )

• -1 < r < +1

• Use for ratio/interval data

Correlation: r is Pos value →

High value of X associated with a High value of Y

Correlation: r is Neg Value →

High value of x associated with low value of Y

Regression

Model that relates one variable (Y) to many variables (X)

• Y = Dependent variable

• X = Independent variables / predictor variables

See regression model ( the formula)

See regression model ( the formula)

Dummy Variables

To include categorical (nominal) variables in a regression by turning categories into 0/1 values.

How do you code a dummy variable

1 = Category is present

0 = Category is absent

Why do we only use d−1 dummy variables for d categories?

To avoid perfect multicollinearity (“dummy variable trap”). One category must be left out as the reference group.

What is the reference category in dummy variables?

The category that is left out. All dummy variable effects are compared to this category.

What happens when D = 0 in the regression

What happens when D = 0 in the regression

Be careful!!

Correlations do not necessarily imply causations

Test of differences

For seeing the difference between things

simplest t test

Two tailed t test

ex. We want to check if the avg/reading score of school A is significantly different the national average

One tailed t test

ex; want to check if the avg reading score of school A is significantly larger than the national average

If you are examing the diffs between 2 variables OR diffs between 2 groups for a single variable

and

you are comparing two or more groups

• 2 groups = Independent samples t test

• >2 groups = ANOVA

Paired t test

Ex. We want to see if the School A boy’s reading scores are different from their scores in writing

• same group/set of people

• diff activities / variables

• often done for before and after scenarios

Independent samples t test

Ex. We want to see if boy’s reading scores are different from girls’ reading scores in School A

• Different groups

• Same activity/variable

ANOVA

When you have more than 2 groups

• Analysis of variance