Stats I Final Pitt 5

statistics performed on nominal/ordinal dependent variables

do not require normality

 one of the most popular nonparametric tests

examines differences in proportions involving either one or two variables

involves only one varaible with 2 or more levels

utilizes two variables with 2 or more levels

1. independence of subjects

2. Not more than 20% of the expected frequencies is less than 5

one of the simplest statistics that can be computed

number of responses (subjects) in a category divided by a total number of responses (subjects)

• 
• where n_i is the number of responses in the i^th category; N is the total number of responses

typically, the population is written as pi,

• positively skewed distribution with ranges from 0 to positive infinity
• -never negative

• critical region of the distribution only appears in teh right side
• -not a directional test

As df increases, the critical value of the distribution decreases

As df incerases, the distribution is less skewed

The mean of X² distribution is equal to df

The variance of the X² distribution is equal to the 2 x df

X² tests have their own distribution

family of distributions denoted by a degrees of freedom

• can be computed using either proportions or frequencies
• -more common to use frequencies of categories

Example: Is there a difference in proportion of people who support and oppose abortion?

often seen as a test of independence (association)

both variables can be DVs or one variable can be a DV while the other is an IV

• Both variables are categorical variables with 2 or more levels
• Variable 1 has c levels and variable 2 has r levels

r = row; c = column

O_ij will have a double subscript to indicate position in table

• dot in 1st subscript = row total
• dot in 2nd subscript = column total

• used to measure effect size in a two way X²
• -can only be used in a 2 x 2

range from 0 to 1

• similar interpretation as r

• used to measure effect size in a two way X²
• - larger than a 2 x 2 design

range from 0 to 1

similar interpretation as r

even though the assumption is on the expected frequencies, there is a higher chance of violating the assumption when the number of participants is small

for a two-way X² test with dichotomous variables (i.e. 2 X 2) where the assumption is most often violated

when the test statistic becomes inaccurate

2 x 2

w = phi

w = (Cramer's V)(square root of q)

(categorical)

Test of marginal homogeneity can be performed to examine a change in categorical variable from time 1 to 2 (within-subjects [repeated measures] design).

test of homogeneity for a dichotomous variable

corrects for continuity

df = 1