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Final Study Guide

# Final Study Guide - Mean 2 sX = Standard deviation for...

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Mean Standard deviation for population, From SS Standard deviation for sample, From SS Sum of squares for population, defn form Sum of squares for population, comp form Sum of squares for sample Sum of squares for sample Computational Form Z-score to raw score Raw score to z-score Single Sample z-test: test statistic z X = Ξ - μ σ Ξ Single Sample z-test: standard error σ X = s 2 n Single Sample t-test: test statistic t X = Ξ - μ σ Ξ Single Sample t-test: estimated standard error s X = σ 2 ν Single Sample t-test:sample variance s 2 = ΣΣ δφ Single Sample t-test: estimated Cohen’s d Estimated Cohen's d = Ξ - μ σ Dependent samples t-test: test statistic: t X D = Ξ σ Ξ Dependent samples t-test: estimated standard error s X D = σ 2 ν Dependent samples t-test: sample variance: s D 2 = ΣΣ δφ Dependent samples t-test: sample SS defn formula SS D = Σ( Ξ ι - Ξ 29 2 Dependent samples t-test: sample SS comp formula SS D = Σ Ξ ι 2 - Σ Ξ ι ( 29 2 ν Dependent samples: estimated Cohen’s d Estimated Cohen's d = Ξ σ 2 Independent samples t-test: test statistic t ( X 1 - Ξ 2 29 = ( Ξ 1 - Ξ 2 29 σ ( Ξ 1 - Ξ 2 29 Independent samples t-test: Pooled variance s p 2 = ΣΣ 1 + ΣΣ 2 δφ 1 + δφ 2 Independent samples t-test: estimated standard error s ( X 1 - Ξ 2 29 = σ π 2 ν 1 + σ π 2 ν 2

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Independent samples: estimated Cohen’s d Estimated Cohen's d = Ξ 1 - Ξ 2 σ π 2 Power Calculation Formulas for z-tests Critical value of the mean: X critical = μ νυλλ + ζ χριτιχαλ σ Ξ z relative to distribution of z under the alternative hypothesis: z = Ξ χριτιχαλ - μ αλτερνατιωε σ Ξ Confidence Interval for a single population mean μ = X ± t conf × s X Confidence Interval for a difference in pop means μ 1 - μ 2 = ( X 1 - X 2 ) ± t conf × s ( X 1 - X 2 ) Confidence Interval for a pop of difference scores μ D = ( X D ) ± t conf × s X D Chi-square test statistic χ observed 2 = ( f o - f e ) 2 f e Linear Least Squares Solution ˆ Y = bX + a , b = SP SS X , a = Y - b X Sum of Squares for X SS X = ( X i - X ) 2 Sum of Cross Products - Definitional Form SP = ( X i - X )( Y i - Y ) Sum of Cross Products - Computational Form SP = Σ ( X i Y i ) - ( Σ X i )( Σ Y i ) n Pearson Correlation Coefficient r = SP SS X SS Y Confounding variable : extraneous variable that correlates with DV and IV Constructs : internal attributes/char that can’t be directly observed Operational : measure external behavior so measurements can be used to infer the status of underlying construct bar chart : discrete data w/ nominal or ordinal scale Line chart : discrete data w/ interval ratio scale Scatter plots: continuous or discrete data w/ both variables of interval or ratio scale Frequency distributions (histograms): continuous data Shape of distributions: symmetry (a/symmetric) and skew (pos-tail right, neg- tail left) Measures of central tendency Mean : interval or ratio scale (NOT nominal or ordinal), pop (u=∑X/N), sample (M, X)
Median : ordinal/interval/nominal; when data is skewed or there’s extreme scores (outliers) Mode

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Final Study Guide - Mean 2 sX = Standard deviation for...

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