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23 Cards in this Set
- Front
- Back
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Variance
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The mean of all squared deviation scores.
ơ^2=(SS)/N (population) s^2=SS/(n-1) (sample) |
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Standard Deviation
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√variance
A rough measure of the average amount by which scores deviate on either side of the mean. Most distributions: 1SD=68%, 2SD=95%, 3SD=99% ơ=√(SS/N)(population) s=√(SS/n-1)(sample) |
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Sum of Squares
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The sum of squared deviation scores.
SS=Σ(X-μ)^2 SS=ΣX2 – (ΣX)^2/N |
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Degrees of Freedom
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The number of values free to vary, given one or more mathematical restrictions.
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Interquartile Range
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The range for the middle 50% of all scores
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z score
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A unit-free, standardized score that, regardless of the original units of measurement, indicates how many standard deviations a score is above or below the mean of its distribution.
z=(X-μ)/ơ |
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Standard Normal Curve
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Always has a mean of 0 and a SD of 1. Area under the curve equals 1.
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Standard Score
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A unit-free score expressed relative to a known means and a known SD. Transformed standard scores are unit-free standard scores that lack negative signs and decimal points (for example, T scores).
z’= desired mean + (z)(desired SD) |
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Upper and Lower Bound of a 95% Confidence Interval
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Mean +/- (1.96 x SE)
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z-scores of 95%, 99%, and 99.9%
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+/-1.96, +/-2.58, +/-3.29
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Pearson Correlation Coefficient (r)
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A number between -1 and 1 that describes the strength and direction of the linear relationship between pairs of quantitative variables.
r=(SPsubxy)/√(SSsubx*SSsuby) where SPsubxy= ΣXY-[(ΣX●ΣY)/n] When used to measure effect ±0.1 is a small effect, ±0.3 is a medium effect, and ±0.5 is a large effect. |
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Assumptions of Pearson Correlation Coefficient (r)
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1. Variables are linearly related.
2. Data are interval or ratio. 3. If measuring significance, data should be normally distributed (although one of the variables can be categorical if there are only two categories) |
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Bivariate correlations
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Correlation between two variables.
Examples: Pearson’s r, Spearman’s rho |
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Partial correlations
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Looks at the relationship between two variables while controlling for a third variable.
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r^2
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Pearson’s correlation coefficient squared. r^2 is the amount (percentage) of variance in one variable that is explained by another.
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rsub-s
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Spearman’s correlation coefficient. A non-parametric statistic computed by first ranking the data and then applying Pearson’s equation to those ranks.
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τ
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Kendall’s tau. A non-parametric correlation used rather than Spearman’s rs when you have a small data set with a large number of tied ranks. Probably more accurate than Spearman’s statistic.
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Biserial (rb) &
Point-Biserial (rpb) Correlation Coefficients |
Correlation coefficient used when one of the two variables is dichotomous. The point-biserial correlation coefficient r¬pb, is used when one variable is a discrete dichotomy whereas the biserial correlation coefficient rb, is used when one variable is a continuous dichotomy.
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Standard error
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Can be calculated by dividing the sample SD by the square root of the sample size (N)
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What are the assumptions of parametric data?
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1. Normally distributed data
2. Homogeneity of variance 3. Interval data 4. Independence |
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What does the assumption of "homogeneity of variance" mean?
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It means that as you go through levels of one variable, the variance of the other should not change. The variance of one variable should be stable at all levels of the other variable.
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How do you test for homogeneity of variance?
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Can use Levene's statistic (want it to be NS). Also can use the variance ratio (especially with large sample sizes), which is the ratio of the variances between the group with the biggest variance and the group with the smallest variance. If the ratio is less than 2 it is safe to assume homogeneity of variance.
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What is the formula for the covariance of variables x & y?
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cov(x,y)= SUM(X-MeanX)(Y-MeanY)/(N-1)
A positive covariance indicates that as one variable deviates from the mean, the other variable deviates from the mean in the same direction. |
