Commonly Used Statistics in the Social Sciences

Chi-squareCorrelationMultiple RegressionT-testsANOVAs

Chi-square (2)Used with nominal scale data Frequency data: number of participants who fall in each of

several categories Can be used with experimental or correlational method Examines the extent to which the frequencies that are

observed in your study differ from the expected frequencies.

Example Null hypo: There is no relationship between sex and hand

dominance. Alt hypo: There is a relationship between sex and hand

dominance.

2 (1, n = 100) = 34.55, p< .01

CorrelationMeasures the degree and direction of linear relationship between 2 variables

Closer to 1 or –1 means stronger relationship Positive value indicates positive relationship, negative value is

negative relationship

The Pearson Correlation Coefficient (r) Used when data is interval or ratio (IQ and height) r (98) = .44, p< .05

Alternative correlation are used when: Both variables are dichotomous (Gender & Handedness) One variable is continuous and one is dichotomous (Gender

and IQ) Both variables are ordinal (ranked color preference and ranked

music preference)

Positive Correlations

As one variable goes up the other one goes up as well

STRONG (r = 1.0) WEAKER ( r= .60)

Negative Correlations

As one variable goes up the other one goes DOWN

STRONG (r = -1.0) WEAKER ( r= -.60)

Multiple RegressionUsed to examine the relationship between two or more predictor variables (IVs) and a criterion variable (DV). Example: Predictor variables: Gender and Age Criterion variable: Income

Multiple regression allows us to control for the effect of 1 IV when examining effects of anotherBeta weight: Standardized units showing the effect of each IV on the

DV when all IVs are in the equation. =.22, p < .05; = .42, p < .01

T-testUsed to examine if 2 groups are significantly different from each other

The DV must have been measured on either interval or ratio scales Can use with between subjects groups (independent samples t-

test) or within subjects groups (paired sample t-test)

Example: Null hypo:

People with brain injuries in the right cerebral hemisphere perform just as well on a standardized spatial skills task as non-injured people.

Alternative hypo: People with brain injuries perform worse than non-injured people.

t (48) = 10.15, p < .05

Analysis of Variance (ANOVA)

Used to determine whether there is a significant difference between groups that have been measured on either interval or ratio scales Can be used with between, within, or

mixed designs! Can be used with 1 or more IVs.

One-way ANOVA

1 independent variable: Physical distance and self-disclosure

IV: Distance of interviewer: Near or far DV: Number of disclosing statements

made ANOVA results

Tell us if distance had an effect Look at means to see what the effect was

F (1, 60) = 14.55, p< .05

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One-way ANOVA

1 independent variable:

More than 2 levels Lets say IV had 3 levels: Near, Medium, Far Can still use the ANOVA!

ANOVA results Tell us if distance had an effect F (2, 60) = 14.55, p< .05) But we don’t know exactly where the differences lie

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Concept Check

A researcher gives some participants alcohol and others an alcohol-like placebo. She then measures their performance on a driving simulation. What statistical test should she use to determine if the participants given alcohol drove worse?

Two-way ANOVA2 Independent Variables (Two way ANOVA): Intelligence and teaching method on academic

performance IVs:

Intelligence: Low and High Teaching method: Traditional or new

DV: Exam performance ANOVA results:

Main effect of intelligence: Was test performance affected by students intelligence? (F (1, 32) = 7.55, p< .05)

Main effect of teaching style: Was test performance affected by teaching style? (F (1, 32) = 8.12, p< .05)

Interaction: Was the effect of teaching style dependent on the students intelligence? (F (1, 32) = 9.32, p< .05)