Two Categorical Variables
Data
We will be working with Electric Vehicle Population Data
Download the clean data set and set up your analysis environment.
Question
Are electric car makes more common in some states versus others?
Contingency Table
ACURA ALFA ROMEO AUDI AZURE DYNAMICS BENTLEY BMW BRIGHTDROP CADILLAC
AE 0 0 0 0 0 1 0 0
AK 0 0 0 0 0 0 0 0
AL 0 0 0 0 0 0 0 0
AP 0 0 0 0 0 1 0 0
AR 0 0 0 0 0 0 0 0
AZ 0 0 0 0 0 0 0 0
BC 0 0 0 0 0 0 0 0
CA 0 0 0 0 0 4 0 0
CO 0 0 1 0 0 2 0 0
CT 0 0 0 0 0 0 0 0
DC 0 0 0 0 0 1 0 0
DE 0 0 0 0 0 0 0 0
FL 0 0 0 0 0 0 0 0
GA 0 0 0 0 0 0 0 0
HI 0 0 0 0 0 0 0 0
ID 0 0 0 0 0 0 0 0
IL 0 0 2 0 0 0 0 0
IN 0 0 0 0 0 0 0 0
KS 0 0 0 0 0 0 0 0
KY 0 0 0 0 0 0 0 0
LA 0 0 0 0 0 0 0 0
MA 0 0 0 0 0 0 0 0
MD 0 0 1 0 0 2 0 1
ME 0 0 0 0 0 0 0 0
MI 0 0 0 0 0 0 0 0
MN 0 0 0 0 0 0 0 0
MO 0 0 0 0 0 0 0 0
MS 0 0 0 0 0 0 0 0
NC 0 0 0 0 0 0 0 0
NE 0 0 1 0 0 0 0 0
NH 0 0 0 0 0 0 0 0
NJ 0 0 0 0 0 0 0 0
NM 0 0 0 0 0 0 0 0
NS 0 0 0 0 0 0 0 0
NV 0 0 0 0 0 0 0 0
NY 0 0 0 0 0 0 0 0
OH 0 0 0 0 0 1 0 0
OK 0 0 0 0 0 1 0 0
OR 0 0 0 0 0 2 0 0
PA 0 0 0 0 0 0 0 0
RI 0 0 0 0 0 0 0 0
SC 0 0 0 0 0 0 0 0
TN 0 0 1 0 0 1 0 0
TX 0 0 0 0 0 0 0 0
UT 0 0 0 0 0 0 0 0
VA 0 0 1 0 0 2 0 0
WA 175 95 4279 4 5 9487 5 1106
WI 0 0 0 0 0 0 0 0
WY 0 0 0 0 0 0 0 0
CHEVROLET CHRYSLER DODGE FIAT FISKER FORD GENESIS GMC HONDA HYUNDAI
AE 0 0 0 0 0 0 0 0 0 0
AK 0 0 0 0 0 0 0 0 0 0
AL 1 0 0 0 0 0 0 0 0 0
AP 0 0 0 0 0 0 0 0 0 0
AR 0 0 0 0 0 1 0 0 0 0
AZ 0 1 0 0 0 0 0 0 0 0
BC 0 0 0 0 0 0 0 0 0 0
CA 3 8 0 0 0 10 1 0 1 2
CO 0 2 0 0 0 1 0 0 0 0
CT 1 3 0 0 0 1 0 0 0 0
DC 0 0 0 0 0 1 0 0 0 0
DE 0 0 0 0 0 0 0 0 0 0
FL 0 0 0 0 0 0 0 0 0 0
GA 1 0 0 0 0 3 0 0 0 1
HI 1 0 0 0 0 0 0 0 0 0
ID 0 0 0 0 0 1 0 0 0 0
IL 0 1 0 0 0 0 0 0 0 0
IN 0 0 0 0 0 0 0 0 0 0
KS 0 1 0 0 0 1 0 0 0 0
KY 0 1 0 0 0 1 0 0 0 0
LA 0 0 0 0 0 0 0 0 0 0
MA 0 1 0 0 0 0 0 0 0 1
MD 3 1 0 0 1 2 0 0 1 1
ME 0 1 0 0 0 0 0 0 0 0
MI 1 0 0 0 0 0 0 4 0 0
MN 0 0 0 0 0 0 0 0 0 0
MO 0 0 0 0 0 0 0 0 0 0
MS 0 0 0 0 0 0 0 0 0 0
NC 1 0 0 0 0 1 0 0 0 0
NE 0 1 0 0 0 1 0 0 0 0
NH 0 0 0 0 0 0 0 0 0 0
NJ 1 0 0 0 0 0 0 0 0 1
NM 0 0 0 0 0 0 0 0 0 0
NS 0 0 0 0 0 0 0 0 0 0
NV 2 1 0 0 0 1 0 0 0 0
NY 0 0 0 0 0 0 0 0 0 0
OH 0 0 0 0 0 0 0 0 0 0
OK 0 0 0 0 0 0 0 0 0 0
OR 0 0 0 0 0 0 0 0 0 1
PA 0 0 0 0 0 0 0 0 0 0
RI 0 0 0 0 0 1 0 0 0 0
SC 1 1 0 0 0 1 0 0 0 0
TN 0 0 0 0 0 0 0 0 0 0
TX 2 2 1 0 0 2 0 0 0 1
UT 0 0 0 0 0 0 0 0 0 0
VA 7 1 0 0 0 2 0 0 0 3
WA 16894 3747 765 770 180 12430 337 334 2001 7207
WI 0 0 0 0 0 0 0 0 0 0
WY 0 0 0 0 0 0 0 0 0 0
JAGUAR JEEP KIA LAMBORGHINI LAND ROVER LEXUS LINCOLN LUCID MAZDA
AE 0 0 0 0 0 0 0 0 0
AK 0 0 0 0 0 0 0 0 0
AL 0 0 0 0 0 0 0 0 0
AP 0 0 0 0 0 0 0 0 0
AR 0 0 0 0 0 0 0 0 0
AZ 0 0 0 0 0 0 0 0 0
BC 0 0 0 0 0 0 0 0 0
CA 0 4 1 0 1 0 0 0 0
CO 0 0 0 0 0 0 0 0 0
CT 0 0 0 0 0 0 0 0 0
DC 0 0 0 0 0 0 0 0 0
DE 0 0 0 0 0 0 0 0 0
FL 0 1 1 0 0 0 0 0 0
GA 0 0 0 0 0 1 0 0 0
HI 0 3 1 0 0 0 0 0 0
ID 0 0 0 0 0 0 0 0 0
IL 0 1 0 0 0 0 0 0 0
IN 0 0 0 0 0 0 0 0 0
KS 0 0 0 0 0 0 0 0 0
KY 0 0 0 0 0 0 0 0 0
LA 0 0 0 0 0 0 0 0 0
MA 0 0 0 0 0 0 0 0 0
MD 0 0 0 0 0 1 0 0 0
ME 0 0 0 0 0 0 0 0 0
MI 0 0 0 0 0 0 0 0 0
MN 0 0 0 0 0 0 0 0 0
MO 0 1 1 0 0 0 0 0 0
MS 0 0 0 0 0 0 0 0 0
NC 0 1 0 0 0 0 0 0 0
NE 0 0 0 0 0 0 0 0 0
NH 0 0 0 0 0 0 0 0 0
NJ 0 0 0 0 0 0 0 0 0
NM 0 1 0 0 0 0 0 0 0
NS 0 0 0 0 0 0 0 0 0
NV 0 0 0 0 0 0 0 0 0
NY 0 0 2 0 0 0 0 0 0
OH 0 0 0 0 0 0 0 0 0
OK 0 0 0 0 0 0 0 0 0
OR 0 0 0 0 0 0 0 0 0
PA 0 1 0 0 0 0 0 0 0
RI 0 0 0 0 0 0 0 0 0
SC 0 0 0 0 0 0 0 0 0
TN 0 1 0 0 0 0 0 0 0
TX 0 2 0 0 0 0 0 0 0
UT 0 0 0 0 0 0 0 0 0
VA 0 4 3 0 0 0 0 0 0
WA 239 5900 11215 5 116 913 356 374 980
WI 0 0 0 0 0 0 0 0 0
WY 0 0 0 0 0 0 0 0 0
MERCEDES-BENZ MINI MITSUBISHI MULLEN AUTOMOTIVE INC. NISSAN POLESTAR
AE 0 0 0 0 0 0
AK 0 0 0 0 0 0
AL 0 0 0 0 0 0
AP 0 0 0 0 0 0
AR 0 0 0 0 0 0
AZ 1 0 0 0 0 0
BC 0 0 0 0 0 0
CA 1 0 0 0 1 1
CO 0 0 0 0 0 0
CT 0 0 0 0 0 0
DC 0 0 0 0 1 0
DE 0 0 0 0 0 0
FL 1 0 0 0 0 0
GA 0 0 0 0 1 0
HI 0 0 0 0 0 0
ID 0 0 0 0 0 0
IL 0 0 0 0 0 0
IN 0 0 0 0 0 0
KS 0 0 0 0 0 0
KY 0 0 0 0 0 0
LA 0 0 0 0 0 0
MA 1 0 0 0 0 0
MD 0 0 0 0 1 0
ME 0 0 0 0 0 0
MI 0 0 0 0 0 0
MN 0 0 0 0 0 0
MO 0 0 0 0 0 0
MS 0 0 0 0 0 0
NC 0 0 0 0 0 0
NE 0 0 0 0 0 0
NH 0 0 0 0 0 0
NJ 0 0 0 0 1 0
NM 0 0 0 0 0 0
NS 0 0 0 0 0 0
NV 1 0 0 0 0 0
NY 0 0 0 0 0 0
OH 0 0 0 0 1 0
OK 0 0 0 0 0 0
OR 0 0 0 0 0 0
PA 1 0 0 0 0 0
RI 0 0 1 0 1 0
SC 0 0 0 0 0 0
TN 0 0 0 0 0 0
TX 0 0 0 0 1 0
UT 0 0 0 0 0 0
VA 0 0 0 0 2 0
WA 2331 1107 1094 2 15447 1225
WI 0 0 0 0 0 0
WY 0 0 0 0 0 0
PORSCHE RAM RIVIAN ROLLS-ROYCE SMART SUBARU TESLA TH!NK TOYOTA VINFAST
AE 0 0 0 0 0 0 0 0 0 0
AK 0 0 0 0 0 0 1 0 0 0
AL 0 0 0 0 0 0 4 0 2 0
AP 0 0 0 0 0 0 0 0 0 0
AR 0 0 1 0 0 0 0 0 0 0
AZ 0 0 1 0 0 0 4 0 0 0
BC 0 0 0 0 0 0 1 0 0 0
CA 0 0 2 0 0 0 66 0 5 0
CO 0 0 1 0 0 1 6 0 1 0
CT 0 0 0 0 0 0 2 0 1 0
DC 0 0 0 0 0 0 1 0 0 0
DE 0 0 0 0 0 0 1 0 0 0
FL 0 0 2 0 0 0 10 0 1 0
GA 0 0 1 0 0 0 3 0 1 0
HI 0 0 0 0 0 0 2 0 0 0
ID 0 0 1 0 0 0 1 0 0 0
IL 0 0 0 0 0 0 3 0 0 0
IN 0 0 0 0 0 0 1 0 0 0
KS 0 0 0 0 0 0 5 0 0 0
KY 0 0 1 0 0 0 1 0 0 0
LA 0 0 0 0 0 0 1 0 0 0
MA 0 0 0 0 0 0 5 0 0 0
MD 0 0 0 0 0 0 17 0 2 0
ME 0 0 0 0 0 0 0 0 1 0
MI 0 0 0 0 0 0 0 0 1 0
MN 0 0 0 0 0 0 1 0 0 0
MO 0 0 0 0 0 0 6 0 0 0
MS 0 0 0 0 0 0 1 0 0 0
NC 0 0 0 0 0 0 13 0 2 0
NE 0 0 0 0 0 0 0 0 0 0
NH 0 0 0 0 0 0 1 0 0 0
NJ 0 0 0 0 0 1 3 0 1 0
NM 0 0 0 0 0 0 0 0 0 0
NS 0 0 0 0 0 0 1 0 0 0
NV 0 0 0 0 0 0 7 0 0 0
NY 0 0 0 0 0 0 9 0 1 0
OH 0 0 0 0 0 0 2 0 0 0
OK 0 0 0 0 0 0 0 0 0 0
OR 0 0 0 0 0 0 2 0 3 0
PA 0 0 0 0 0 0 3 0 0 0
RI 0 0 1 0 0 0 0 0 0 0
SC 0 0 0 0 0 0 3 0 0 0
TN 0 0 0 0 0 0 1 0 0 0
TX 0 0 1 0 0 0 16 0 2 0
UT 0 0 0 0 0 0 2 0 0 0
VA 0 0 1 0 0 1 28 0 4 0
WA 1433 2 6699 4 241 1912 99456 5 9237 2
WI 0 0 0 0 0 0 1 0 0 0
WY 0 0 0 0 0 0 1 0 0 0
VOLKSWAGEN VOLVO WHEEGO ELECTRIC CARS
AE 0 0 0
AK 0 0 0
AL 1 0 0
AP 0 0 0
AR 0 0 0
AZ 0 1 0
BC 0 0 0
CA 4 1 0
CO 0 3 0
CT 0 1 0
DC 0 0 0
DE 0 0 0
FL 0 0 0
GA 1 1 0
HI 0 0 0
ID 0 0 0
IL 1 0 0
IN 0 0 0
KS 0 1 0
KY 1 0 0
LA 0 0 0
MA 0 0 0
MD 1 1 0
ME 0 0 0
MI 0 0 0
MN 0 0 0
MO 0 0 0
MS 0 0 0
NC 0 0 0
NE 0 0 0
NH 0 0 0
NJ 0 1 0
NM 1 0 0
NS 0 0 0
NV 0 0 0
NY 0 0 0
OH 0 0 0
OK 0 0 0
OR 0 0 0
PA 0 0 0
RI 0 0 0
SC 0 0 0
TN 0 0 0
TX 0 0 0
UT 0 0 0
VA 1 2 0
WA 5848 5782 3
WI 0 0 0
WY 0 0 0Hypothesis testing – Chi-squared
Chi-square (\(\chi^2\)) – statistical test that determines if there’s a significant association between categorical variables
Chi-square test for independence: Tests whether two categorical variables are related to each other
Hypothesis testing – Chi-squared
\(H_0\): Observed frequencies match expected frequencies. There is no deviation from expected values, hence there is no relationship between the two categorical variables.
Pearson's Chi-squared test
data: my_table
X-squared = 2855.8, df = 2160, p-value < 2.2e-16Since the p value is less than the alpha of 0.05, we can reject the null hypothesis.
Visualization
Bivariate hypothesis testing – summary
- one categorical with two groups and one numeric variable: t-test
- one categorical and one numeric variable: ANOVA
- two numeric variables: correlation
- two categoric variables: chi-squared
Gradescope activity
Questions
What other questions can you answer based on this data set?