Create two sample data vectors, containing three and four distinct values, respectively.

x = [1 1 2 3 1];
y = [1 2 5 3 1];

Cross-tabulate x and y.

table = crosstab(x,y)

table = 3×4

     2     1     0     0
     0     0     0     1
     0     0     1     0

The rows in table correspond to the three distinct values in x, and the columns correspond to the four distinct values in y.

Generate two independent vectors, x1 and x2, each containing 50 discrete uniform random numbers in the range 1:3.

rng default;  % for reproducibility
x1 = unidrnd(3,50,1);
x2 = unidrnd(3,50,1);

Cross-tabulate x1 and x2.

[table,chi2,p] = crosstab(x1,x2)

table = 3×3

     1     6     7
     5     5     2
    11     7     6

chi2 = 7.5449

p = 0.1097

The returned p value of 0.1097 indicates that, at the 5% significance level, crosstab fails to reject the null hypothesis that table is independent in each dimension.

Load the sample data, which contains measurements of large model cars during the years 1970-1982.

load carbig

Cross-tabulate the data of four-cylinder cars (cyl4) based on model year (when) and country of origin (org).

[table,chi2,p,labels] = crosstab(cyl4,when,org);

Use labels to determine the index location in table for the number of four-cylinder cars made in the USA during the late period of the data.

labels

labels=3×3 cell array
    {'Other'   }    {'Early'}    {'USA'   }
    {'Four'    }    {'Mid'  }    {'Europe'}
    {0x0 double}    {'Late' }    {'Japan' }

The first column of labels corresponds to the data in cyl4, and indicates that row 2 of table contains data on cars with four cylinders. The second column of labels corresponds to the data in when, and indicates that column 3 of table contains data on cars made during the late period. The third column of labels corresponds to the data in org, and indicates that location 1 of the third dimension of table contains data on cars made in the USA.

Therefore, table(2,3,1) contains the number of four-cylinder cars made in the USA during the late period.

table(2,3,1)

ans = 38

The data contains 38 four-cylinder cars made in the USA during the late period.

Create a contingency table from data, and visualize the table in a heatmap chart.

Load the hospital data.

load hospital

The hospital dataset array contains data on 100 hospital patients, including last name, gender, age, weight, smoking status, and systolic and diastolic blood pressure measurements.

Convert the dataset array to a MATLAB® table.

Tbl = dataset2table(hospital);

Determine whether smoking status is independent of gender by creating a 2-by-2 contingency table of smokers and nonsmokers, grouped by gender.

[conttbl,chi2,p,labels] = crosstab(Tbl.Sex,Tbl.Smoker)

conttbl = 2×2

    40    13
    26    21

chi2 = 4.5083

p = 0.0337

labels = 2x2 cell
    {'Female'}    {'0'}
    {'Male'  }    {'1'}

The rows of the resulting contingency table conttbl correspond to patient gender, with row 1 containing data for females and row 2 containing data for males. The columns correspond to patient smoking status, with column 1 containing data for nonsmokers and column 2 containing data for smokers. The returned result chi2 = 4.5083 is the value of the chi-squared test statistic for a Pearson's chi-squared test of independence. The $\mathit{p}$-value for the test p = 0.0337 suggests, at a 5% level of significance, rejection of the null hypothesis that gender and smoking status are independent.

Visualize the contingency table in a heatmap. Plot smoking status on the $\mathit{x}$-axis and gender on the $\mathit{y}$-axis.

heatmap(Tbl,'Smoker','Sex')