Week Six - Chi-Square Flashcards
What is a Univariate Design
One variable
What is a Factorial Design
Two or more variables
Explain Degrees of Freedom
In statistics, the number of degrees of freedom is the number of values in the calculation of a final statistic that are free to vary.
Example: If three numbers sum to 30, how many degrees of freedom are there? How many numbers can be chosen at random?
- 2
What are inferential stats?
Inferential statistics answer questions about whether statistics from a sample generalise to a population.
What do Descriptive stats do?
[Descriptive] statistics summarise data
What is an Effect Size
A [usually standardised] measure of the strength of relationship or magnitude of difference among a set of statistics.
Allows an assessment of practical significance
Chi-square tests can only be used with what type of data?
CHI-SQUARE TESTS CAN ONLY BE USED WITH CATEGORICAL (OR ORDINAL) DATA.
A Chi-Square Goodness of Fit is what kind of test?
univariate
What are we doing when conducting a CSGOF? i.e., What does it test?
When conducting a Chi-square Goodness-of-Fit test, we are examining a single variable and testing whether the counts (or percentages) in the different categories for
that variable differs significantly from a uniform distribution.
What is the Null Hypothesis for CSGOF?
Default assumption for null hypothesis is that the population is uniformly distributed across categories.
Proportions are equal for all levels of the variable.
What are the 3 Chi-Square Data Assumptions?
Counts in each category (cell) must be independent
A single observation cannot contribute to more than one category
Data must be counts (categorical or ordinal variable)
Number of observations in each category
Sample size must be large enough
Expected frequencies (counts) in all cells should be at least 5
Observed frequencies can be less than 5.
How do you calculate degrees of freedom for a chi-square goodness of fit?
Number of cells - 1
What does a Chi-square measure?
CHI-SQUARE MEASURES HOW WELL THE DATA MATCH (FIT) THE EXPECTED DISTRIBUTION
Small chi square stat means? and is dependent on?
good fit
0 = good fit and closer to null
Magnitude of Chi-square statistic is dependent on
Sample size
Degrees of freedom
Chi-square formula is
X^2 = sum of all cells (observed count-expected count)^2/expected count
What does Cramer’s V do?
Tells us how big the difference is between the observed data and the null hypothesised expected data.
Cramer’s V =
Square root of X2(chi stat)/N(k-1)
- N = total sample size
- K = levels of variable
Cramer’s V stats
> .5 = large
.3-.5 = medium
.1 - .3 = small
0 -.1 = trivial
Chi-Square GOF write up looks like
χ 2 (dof, N = (sample size)) = STAT (CS result), p = , Cramer’s V = ..
Chi-Square Test of Independence Tests what
whether two categorical variables are independent
When we conduct a chi-square test of independence, we’re comparing groups in terms of some outcome variable. For example, you might be comparing two groups of students (those who ate breakfast and those who didn’t) in terms of propensity to fall asleep in class.
The Null Hypothesis for CSTOI
Do the proportions within the levels of one or more categories deviate significantly from the total proportions
Expected proportions will be equal
NULL = There is no relationship between the variables
Calculation for Expected Frequencies
Expected Frequency = (Rowtotal x Columntotal)/Ntotal
For a Chi-square Test-of-Independence expected degrees of freedom are calculated using what formula?
df = (R-1) x (C-1)
What test do we use if expected frequencies are bloew 5
USE FISHER’S EXACT TEST OR ROBUST IF BELOW 5
A test becomes robust when?
fewer than 20% of cells have small expected frequencies
