Two Sample Data → 3 possible t-test options
-Option 1: Unpaired Data, Independent with Equal Variance
-the individuals in each sample are not related to each other (simple randomization took place) + equal variance
Notation + Formulas:
df = n1 + n2 -2
-Option 2: Unpaired Data, Independent with UNEQUAL Variance (df ≈ smaller of the two sample sizes - 2)
-degrees of freedom given: …
-Option 3: Paired Data, Dependent: each participant has another participant connected to them in the other group, results
are taken for same person at two different times, two participants from separate groups are matched based on similar
characteristics—--For this test, we must compare the differences between the pairs
Notation:
-µd=mean of the paired differences for the population
-d bar=mean of the paired differences for the sample
-sd=standard deviation of the paired differences for the sample
-sd bar=standard error of the t distribution
-n=number of pairs
Formulas: ↓
-degrees of freedom: n (the # of pairs) - 1
-note: if two tailed, divide α by 2 to find the critical value
Correlation with t distribution, Use this test when:
-testing whether the association between two variables is statistically significant
Notation:
-r = the observed value
-0 = the hypothesized value in H0
-standard deviation = 1 − 𝑟2
Formulas:
-n = sample size, df = n-2
-note: two-tailed, divide α by 2 to find the critical
value on the t distribution
ANOVA Test, always right tailed, use when comparing 3 or more groups
-to read F distribution table, you need df for numerator and
denominator, and significance level
df(total)=total sample size-1
H0: µ1 = µ2 = µ3 (must label group)
Ha: µ1≠µ2 or µ1≠µ3 or µ2≠µ3 or µ1≠µ2≠µ3
df(B) = numerator, df(W) = denominator
←Bivariate Regression (assume normality(both var’s approx normal), linearity, indep of error)
b0: Based on the model, the predicted value of y-variable for individuals with a
x-variable score of 0 would be ____.
b1: For every 1-point increase in x-variable scores, the predicted value of y-variable
will increase by ___ points.
H0 : β1 = 0, Ha : β1 ≠ 0 (bivariate regression explains or predicts an outcome)
R2 : approximately __% of the variance in y-variable is associated with the x-variable
Chi-Squared GOF (does observed frequencies match the hypothesized frequencies?)(use χ2 distribution)
specify…H0: the data are consistent with a specified dist., Ha: the data are not…
E (for GOF) = cell proportion • total count
-assumptions: sample values independent, counts, hypothesized distribution given in
advance, random sample
df = # of categories - 1
Chi-Squared Test of Independence (use χ2 distribution) (use same equation as above)
-Assumptions: categorical data, each subject only contributes to 1 cell, random samp., 5+ observations per cell
-E = (column total)(row total)/N
N = total sample size
-df = (rows-1)(columns-1), to use χ2 table find intersection of df and χ2alpha level