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PSYC 305
Heungsun Hwang

1 mean (k=1) Interval or ratio • z test: sample mean vs population mean o Assumptions:  Population is normally distributed  Known mean (µ) and standard deviation of population (σ)  Random sample of the population • t test WHEN POPULATION STD DEV (σ) IS UNKNOWN: sample vs population means o H : µ = (constant for what population mean is) 0 o Assumptions:  Population is normally distributed  Known mean of population (µ)  Random sample of the population o DF = N-1; t (N-1) = ______, p 2 means (k=2) Independent Ordinal • Wilcoxon rank sum test = Mann-Whitney U o H 0 Two samples come from populations with the same continuous distribution. o U = _________, p • Median test (sign test): compares the median of the 2 samples o H 0 No difference exists between the medians of the populations from which the samples are drawn. 2 • Uses sign contingency table and χ o DF = (R-1)(C-1) Interval or ratio • Independent t test: tests mean of 2 unknown populations o H 0 µ1= µ2 o Assumptions:  Population is normally distributed  Variance of the populations are equal  Random sample of the population o DF= N +1 -22; t(N 1N 22) = __________, p Dependent Interval or ratio • Paired t test 3 means (k=3) Independent Nominal • χ (tests independence of nominal variables) o H : Two (nominally scaled) variables are statistically independent (no association). 0 o Assumptions:  Random samples  Independent observations  A sufficiently large sample size is required (N ≥ 20)  Average cell frequency should be ≥ 5 o Expected frequency: (Row total) * (Column total)/ (sample size) o DF = (R-1)(C-1) Ordinal • Kruskall Wallis H (rank test) o H 0 k independent samples come from the same population. o DF = k-1 when N ≥ j & k ≥ 3. Uses χ distribution o H (k-1) = _________, p o If significant, do a pairwise Kruskall Wallis H test  if p<0.5/k, you get significance • Median test Interval or ratio • One-way ANOVA (compares means of populations) o H 0 μ 1 μ .2. = μ k o Assumptions:  Population is normally distributed within each group  Variance of the populations are equal  Independence of observations o F(k-1, N-k)=________ where F = V /V B W o When H is0rejected, conduct Post-hoc tests (Scheffe and Tukey) to know which pair significantly different: PAIRWISE COMPARISONS!!!!!  Scheffe's Test (For groups of different sizes) MOST CONSERVATIVE • For critical value, need DF(B) = k-1 and DF(W)= N-k multiply by k-1  Tukey's HSD (For groups of equal sizes) • uses Q (studentized range statistic) • Called Tukey-Kramer test when diff sample size o ASSESSING NORMALITY  Plot histograms  Skewness test (H : 0kewness= 0 (for each group)) • t = skewness/ StdError • df = #data per group (n) - 1  QQ plot: data close to normal will lie in a STRAIGHT LINE  K-S test & Shapiro Wilk: compares sample to scores from normal distribution • H 0The scores follow a normal distribution o ASSESSING HOMOGENEITY OF VARIANCE  Fmaxtest of Hartley (For groups of equal sizes): F max= max V/ min V • If equal variance, F = 1 • F(k, n-1)
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