Transcript Chi-Square Test

Chi-Square Test
Chi-Square
2
(χ )
Test
• Used to determine if there is a significant
difference between the expected and
observed data
• Null hypothesis: There is NO statistically
significant difference between expected &
observed data
• Any differences are due to CHANCE alone
Chi-Square
2
(χ )
Formula
How to use the Chi-Square Test
1.
Determine null hypothesis
• All frequencies are equal –OR– Specific frequencies given already
2.
Use formula to calculate χ2 value:
• n = # of categories, e = expected, o = observed
3.
Find critical value using table (Use p=0.05).
• degrees of freedom (df) = n – 1
4.
If χ2 < Critical Value, then ACCEPT null hypothesis. Differences in
data are due to chance alone.
If χ2 > Critical Value, REJECT the null hypothesis: Differences in
data are NOT due to chance alone!
Sample Problem
• You buy a package of M&Ms from the factory store
and find the following: 20 brown, 20 blue, 20 orange,
20 green, and 20 yellow M&Ms.
• According to the M&M website, each package of
candy should have 13% brown, 24% blue, 20%
orange, 16% green, 13% red, and 14% yellow
M&Ms.
• You realize you are missing Red M&M’s in your
package! Is this acceptable, or did something happen
in the factory during the packaging process?
• Use the Chi-Square Test to answer this question.
Warm up – Chi-Square Practice
A high school, students can choose to enter one of three doors.
Custodians noticed that door #3 was always getting broken and
suggested that more students use that door because it has a handsfree opener. Science minded students counted the number of
students entering each door to see if the custodians were right.
 Door #1 had 60 students enter
 Door #2 had 66 students enter
 Door #3 had 80 students enter
Were the custodians’ suspicions supported by the data? Use a ChiSquare Test to support your answer.