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PSYC 305
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Heungsun Hwang
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Midterm

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Psychology

PSYC 305

Heungsun Hwang

Winter

Description

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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