Lectures 1 & 2 (Intro & Testing Assumptions)
for a sufficiently large sample size (n=30), the distribution of the sample means will approximate a normal distribution as n increases
What is the difference between correlation and covariance?
Correlation measures the relationship between two variables standardized z-scores while covariance does the same in raw scores.
What is a moderator?
Moderators show when or how much the IV will affect the DV.
The covariate in ANCOVA analyses should be correlated with the ______ and independent from the _______ variable
dependent; independent
What is a two-way independent ANOVA? What is a three-way independent ANOVA?
A two-way independent ANOVA (also called a factorial ANOVA) examines the effects of two independent variables (factors) on a single dependent variable.A three-way independent ANOVA is the same with three IVs.
In a negatively skewed sample, which statistic would appear first?
A) mode, B) median, or C) mean
C) Mean
"The tail tells the tale"
The mean is most affected by outliers, and the tail appears to the left in negatively skewed data.
A Pearsons correlation of .33 indicates a ____ effect size.
Medium
±.1 = small effect
±.3 = medium effect
±.5 = large effect
Based on this output, is there a significant mediation effect?
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals
Estimate 95% CI Lower 95% CI Upper p-value
ACME 4427.176 3094.002 5598.62 0.002 **
ADE -1469.583 -3318.940 463.13 0.144
TotalEffect2957.593 1227.475 4688.00 <2e16***
Prop.Mediat1.497 0.892 3.45 0.002 **
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Sample Size Used: 90
Simulations: 999
Yes becuase ACME is significant. Full mediation because ADE is not significant.
What does the Bonferroni, Scheffe, and Tukey test do? Which is the most strict?
help control for experimentwise Type I error (reduces culmative probability of false positives across multiple statistical tests)
Bonferroni is the most strict (alpha at .05)
True or false: ANCOVA combines the analysis of variance with regression
True
List factors that affect power.
What do B weights and Beta weights tell us? How are they different?
They represent the unique effect of that predictor on the DV. B weights for raw scores and Beta weights (fancy B) for z-scores.
When would one use a Mann-Whitney U test instead of a Wilcoxon signed-rank test?
Use a Mann-Whitney U (or Wilcoxon rank-sum) when you have independent groups and nonparametric data. Use a Wilcoxon signed-rank test when you have dependent groups and nonparametric data.
What is the Kruskal-Wallis test?
the non-parametric counterpart of the one-way independent ANOVA
When and why do we use a Chi-square goodness of fit test?
To determine if the observed frequencies of a categorical variable match an expected distribution.
used for Goodness of Fit and Test of association
List all the assumptions for a parametric test.
1. Normally distributed sampling distribution
2. Homogeneity of variance/ Homoscedasticity
3. Interval or ratio data
4. Independence of scores.
List all the assumptions for regression.
1. Linearity
2. Normality
3. Independence of scores
4. Independence of errors (errors should not be correlated)
5. Minimal multicollinearity: The predictors (IVs) should not be highly correlated with each other. Rule of thumb is no higher than r = .80 between predictors.
6. Homoscedasticity
Why do we center continuous varibles around the mean in moderation analyses?
To reduce multicolinearity
What does this output tell us?
Anova Table (Type III tests)
Response: ActivityLevel
SumSq Df F value Pr(>F)
(Intercept) 53.542 1 21.9207 9.323e-05 ***
ActivityLevel 17.182 1 7.0346 0.01395 *
dose 36.558 2 7.4836 0.00298 **
PartnerActivityLevel:dose20.427 2 4.1815 0.02767*
Residuals 58.621 24
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The relationship between the partner's activity level and the participant's activity level differs depending on the dose administered.
What is the Cramer's V?
measure of effect size for catergoical variables in ch-squared test. interpreted like Pearson's r.
How can we assess for normality?
Central Limit Theorum, Graphical displays (Q-Q plot, histogram, values of skew and kurtosis, Shapiro-Wilk
What can we say from this output about the variance explained from advertising budgets on sales?
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.341e+02 7.537e+00 17.799 <2e16***
adverts 9.612e-02 9.632e-03 9.979 <2e-16***
Residual standard error: 65.99 on 198 degrees of freedom Multiple R-squared: 0.3346, Adjusted R-squared: 0.3313 F-statistic: 99.59 on 1 and 198 DF, p-value: < 2.2e-16
Advertising budget significantly explained
33.1% of the variance of sales.
What is bootstrapping and why do we use it?
Bootstrapping is a resampling technique that is used when assumptions (like normaility) are broken.
What is a simple effect in a factorial ANOVA?
The variability among treatment means associated with one IV at a particular level of another IV
List two assumptions specific to a chi-squared test.
1. Independence: Each person, item or entity contributes to only one cell of the contingency table.
2. The expected frequencies should be greater than n = 5.