homogenity
What does the chi-square test of homogeneity check for?
It checks whether different groups have the same distribution.
What condition is commonly used to check independence in statistics?
the 10% condition
What does a chi-square goodness of fit test check?
It checks whether the observed distribution matches the expected distribution.
7-1=6
What is Observed Count?
The actual number of observations collected in a category.
What are the hypotheses for a homogeneity test?
What does the 10% condition say?
The sample size must be less than or equal to 10% of the population.
What are the hypotheses for a goodness of fit test?
E=20
What is a Expected Count?
The number of observations expected if the null hypothesis is true.
What condition must be met for expected counts in a homogeneity test?
All expected counts must be greater than or equal to 5.
A population has 2,000 people. Can a sample of 150 people meet the 10% condition?
0.10(2000)=200
Yes, because 150 ≤ 200.
The sample meets the 10% condition.
A goodness of fit test has 6 categories. What are the degrees of freedom?
6-1=5
degree of 5
A die is rolled 60 times. Since a fair die has 6 sides, what is the expected count for each side?
E=10
What is a Chi-Square Statistic?
A value that measures the difference between observed and expected counts.
A cell has a row total of 40, a column total of 30, and a grand total of 120. Find the expected count.
using: (row total)(colum total)/ grand total
= (40)(30)/120=10
A researcher wants to sample 90 students from a school with 800 students.
Does the sample satisfy independence?
0.10(800)=80
No, because 90 > 80.
The sample does NOT satisfy the 10% vundition.
An observed count is 20 and the expected count is 16. Find the chi-square contribution for that category.
(20-16)2/16
= (4)2/16=1
A chi-square test has 5 categories. Find the degrees of freedom.
5-1=4
What is a Degrees of Freedom?
The number of values that are allowed to vary in a statistical calculation.
A table has 3 rows and 4 columns. What are the degrees of freedom?
(3 - 1)(4 - 1) = (2)(3) = 6
So, the degrees of freedom are 6.
A school has 900 students. A researcher surveys 75 students. Does this meet the 10% condition for independence?
0.10(900)=90
Yes.
A chi-square goodness of fit test has 9 categories. What are the degrees of freedom?
9-1=8
An observed count is 25 and the expected count is 20. Find the chi-square contribution for that category.
(25-20)2/20= 25/20=1.25
What does having Independence means?
When one variable does not affect another variable.