Psych 300B: Final Exam Review (Analysis of Frequency Data)

What kind of data, statistical tests and analyzation can be carried out on frequency data

Data - Qualitative and represents nominal scale

Statistical Tests - non-parametric tests (do not estimate population parameters)

Analyzation - dependent on size of sample, type of research design and model of hypothesis testing

What are the two types of analyzation when using random sampling or random assignment

Random Sampling - uses chi-squared test or z-corrected test

Random Assignment - uses binomial or Fisher’s exact

What is the major difference between random sampling and random assignment models

Random sampling gives estimated p-value, while random assignment gives exact value for p(obs)

What are the 3 criteria for all forms of frequency analysis

IV: nominal/ordinal, so has discrete measures

DV: qualitative data and uses frequency counts/tallies where each tally is independent

H0: assumes data are either evenly or proportionally distributed across categories

What does a statistical test for frequency data actually do

Tells us the probability that the distribution of values is random

What does the Chi square statistic report (what is the null in general)

The probability that a distribution of observed frequency are evenly or proportionally distributed across categories

What is the general formula Chi square statistic (χ²)

F(obs) = ∑ (O - E)² / E

O: the observed number of actual tallies

E: the expected number of tallies

What are the 6 major assumptions of the χ² test

1. Each observation is independent

2. Adding all tallies in each category = nT (categories are exhaustive)

3. nT ≥ 20

4. E ≥ 5 for each category

5. Data is qualitative

6. IV measured only on nominal/ordinal scale

What are the two characteristics of the null distribution χ² test

1. Numerically equals a squared z-distribution

2. The x axis ranges from 0 to infinity

What are the 3 characteristics of the shape of the null distribution χ² test

1. Varies with df (family of curves)

2. Positively skewed when df small

3. Becomes more symmetrical as df increases

Why does χ²crit increases as df increases

Because df is based on number of categories not number of people

What are the 4 major types of Chi square statistic tests

1. Simple Design

2. Goodness of Fit

3. Test of Independence

4. Test of Homogeneity

Simple design

k = 1, c = 2, nT ≥ 20

Tests if observed frequencies between two options differs from what was expected

df = c - 1

Goodness of fit

k = 1, c > 2, nT ≥ 20 (E ≥ 5 for each category)

Tests if observed frequencies between 3 or more options differ from what is expected (either proportionally or evenly)

df = c1

Test of independence

k ≥ 2, c ≥ 2 and nT ≥ 20

Single sample test for contingency between variables

df = (# of rows - 1) x (# columns - 1)

Test of homogeneity

k ≥ 2, c ≥ 2 and nT ≥ 20

A multi-sample of the equality of frequency distribution across a single variables

df = (# of rows - 1) x (# columns - 1)

What is H0 for a test of independence and test of homogeneity

Frequency distribution of one categorical variable is not contingent on levels of a second categorical variable

Phi coefficient

Effect size for contingency tables, measures the strength of association between two variables

How is the phi coefficient interpreted

Same as cohen’s effect size

small - 0.10

medium - 0.30

large - 0.50

How is phi calculated for a 2 × 2 and a > 2 × 2 contingency table

2 × 2: φ = √χ²/n

> 2 × 2: φ = √χ²/n(df_s)

df_s = df of smaller dimension