Statistical Tests: Assumptions, Hypotheses, and Test Statistics

Question 1

Univariate z test

Answer 1

Used for testing one binary categorical variable
Assumptions: randomization, sample size > 15 successes and 15 failures
Null: p=#
Alternative: p greater than or less than # (one tailed), p isn’t equal to # (two tailed)

Question 2

Chi square goodness of fit test

Answer 2

One categorical variable with more than 2 categories
Null: p1=#, p2=#
Alternative: at least one Pi doesn’t equal expected value
Test statistic: x^2
Degrees of freedom: # of categories-1

Question 3

Univariate t test

Answer 3

One numerical variable
Assumptions: randomization, approximately normal distribution
Null: mu=#
Alternative: mu greater than or less than # (one tailed), mu isn’t equal to # (two tailed)
Degrees of freedom: n-1

Question 4

Chi square test of independence

Answer 4

Both explanatory and response variable are categorical; at least one has more than 2 categories
Assumptions: randomization, expected cell count is greater than 5 for all cells, cells are independent of each other
Null: Pij= Pi x Pj (2 variables are independent)
Alternative: at least 1 Pij doesn’t equal Pi x Pj
Test statistic: x^2
Degrees of freedom: (# rows - 1) x (# columns - 1)

Question 5

Bivariate z test

Answer 5

Two binary, categorical variables
Assumptions: independent and random sample, more than 5 successes and failures in each group
Null: p1-p2=0
Alternative: p1-p2 doesn't equal 0
Test statistic: z

Question 6

Simple regression

Answer 6

Two quantitative variables
Assumptions: randomization, homoscedasticity (error terms are normally distributed along regression line)
Slope uses t test (null: slope=0, alternative: slope doesn’t equal 0)
Entire model uses f test (null: all slopes equal 0, alternative: at least one slope doesn’t equal 0)

Question 7

Multiple regression

Answer 7

Multiple numeric explanatory variables and one numeric response variable
Assumptions: randomization, homoscedasticity, normal distribution of y, predictors aren’t highly correlated with one another
Slope uses t test (null: slope=0, alternative: slope doesn’t equal 0)
Entire model uses f test (null: all slopes equal 0, alternative: at least one slope doesn’t equal 0)

Question 8

Bivariate, independent t test

Answer 8

One binary, categorical explanatory variable and one numerical response variable
Assumptions: randomization, independent samples, approximately normal distribution
Null: mu1-mu2=0
Alternative: mu1-mu2 doesn’t equal 0
Test statistic: t
Degrees of freedom: n-2

Question 9

Bivariate, dependent t test

Answer 9

One binary, categorical explanatory variable and one numerical response variable
Assumptions: randomization, dependent samples, approximately normal distribution
Null: sum of differences=0
Alternative: sum of differences doesn’t equal 0
Test statistic: t
Degrees of freedom: n-1

Question 10

One-way ANOVA

Answer 10

One categorical explanatory variable with more than 2 categories and one numerical response variable
Assumptions: randomization, independence, normal distribution in population, approximately equal standard distributions
Null: mu1=mu2=mu3…
Alternative: at least 2 mus aren’t equal
Test statistic: f

Question 11

Two-way ANOVA

Answer 11

3 or more categorical explanatory variables and one numerical response variable
Assumptions: randomization, independence, normal distribution in population, approximately equal standard distributions
Null for interaction: no significant interaction
Alternative for interaction: significant interaction
Null for main effects: mu1=mu2=mu3…
Alternative for main effects: at least 2 mus aren’t equal
Test statistic: f