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Commonly Used Statistics in the Social Sciences

Commonly Used Statistics in the Social Sciences. Chi-square Correlation Multiple Regression T-tests ANOVAs. 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

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Commonly Used Statistics in the Social Sciences

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  1. Commonly Used Statistics in the Social Sciences • Chi-square • Correlation • Multiple Regression • T-tests • ANOVAs

  2. 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

  3. Correlation • Measures 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)

  4. Positive Correlations • As one variable goes up the other one goes up as well STRONG (r = 1.0) WEAKER ( r= .60)

  5. Negative Correlations • As one variable goes up the other one goes DOWN STRONG (r = -1.0) WEAKER ( r= -.60)

  6. Multiple Regression • Used 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 another • Beta 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

  7. T-test • Used 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

  8. 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.

  9. 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

  10. 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

  11. 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?

  12. Two-way ANOVA • 2 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)

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