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Unit 8 - Coggle Diagram
Unit 8
Chi-square 2-way Tests (L45)
Two-way table
: a table that organizes frequencies from two categorical variables
chi-square homogeneity
: distributions of a
single
categorical variable across several samples
chi-square independence
: determine associations between two categorical variables
Compare
proportions
because counts are inconsistent among samples of different sizes
Homogeneity
H0: the distribution of the variable is the
same
for the groups/treatments (Ha: "different between groups")
Properties
(for both)
Chi-square statistic
df
= (rows - 1) * (columns - 1)
Expected counts
= (row total) * (column total) / (table total)
Also use large counts instead of normality
Independence
H0: no association between variables (Ha: association between variables)
Chi-square: Goodness of Fit (L44)
One-way table
: table that displays counts for categories of a single categorical variable
Observed counts
: the actual counts from a sample/study
Expected counts
: counts that are expected if H0 is true
GOF Properties
Expected counts = (sample size) * (specified proportion)
Chi-square statistic
Larger
values of x^2 gives more evidence
against
the H0
Third condition is large counts, not normality (because the distribution is
right-skewed
in the first place)
df
= number of categories - 1
mean
of the distribution = df
mode
of the distribution = df - 2
The distribution is approximately
normal when df > 90
Null hypothesis: the distN of the variable is
the same as the claim
(alternative: different from the claim)
Each individual term that produces the test statistic is called a
component
Distinguishing tests
one-way table
: GOF
test whether a
variable is the same
across more than one population/treatments:
homogeneity
test whether
two categorical variables are associated
in the
same sample
: independence