# grpstats

Summary statistics organized by group

## Description

tblstats = grpstats(tbl,groupvars) returns a table with group summary statistics for the variables in the table tbl, where the function determines the groups according to the grouping variables in tbl specified by groupvars.

If all variables in tbl (other than the grouping variables) are numeric or logical, then the summary statistic is the mean of each group for each variable in tbl. Otherwise, the summary statistic is the number of elements in each group. tblstats contains a row for each observed unique value or combination of values in the grouping variables.

tblstats = grpstats(tbl,groupvars,whichstats) specifies the summary statistic types whichstats.

example

tblstats = grpstats(tbl,groupvars,whichstats,Name,Value) specifies additional options using one or more name-value arguments. For example, "DataVars",[2,4] instructs the function to compute summary statistics for the second and fourth variables in tbl.

example

stats = grpstats(X,group) returns an array with group summary statistics for the columns of the matrix X, where the function determines the groups by the grouping variables in group.

If X is a numeric or logical matrix, then the summary statistic is the mean of each group for each column of X. Otherwise, the summary statistic is the number of elements in each group. stats contains a row for each observed unique combination of the grouping variables.

example

[stats1,...,statsN] = grpstats(X,group,whichstats) specifies the summary statistic types whichstats and returns an array for each summary statistic.

example

[stats1,...,statsN] = grpstats(X,group,whichstats,"Alpha",a) also specifies the significance level a for confidence and prediction intervals.

example

grpstats(X,group,alpha) plots the group means of data in the numeric or logical matrix X, grouped by the variables in group. The function also plots the 100×(1 – alpha)% confidence interval for each group mean. The grouping variable values are on the horizontal plot axis.

• If X is a matrix, then grpstats plots the means and confidence intervals for each column of X.

• If group is a cell array of grouping variables, then grpstats plots the means and confidence intervals for the groups determined by the observed unique combinations of the grouping variables.

## Examples

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Compute summary statistics for input data in a table. Group the input data using one or two grouping variables, and specify one or two types of summary statistics to compute.

Create a table that contains the variables Gender, Age, Weight, and Smoker.

tbl = table(Gender,Age,Weight,Smoker);

Gender is a cell array with the two unique values Male and Female. The variables Age and Weight have numeric values, and Smoker has logical values.

Compute the mean for the numeric and logical arrays in tbl grouped by Gender.

tblstats1 = grpstats(tbl,"Gender")
tblstats1=2×5 table
Gender      GroupCount    mean_Age    mean_Weight    mean_Smoker
__________    __________    ________    ___________    ___________

Male      {'Male'  }        47         38.915       180.53         0.44681
Female    {'Female'}        53         37.717       130.47         0.24528

tblstats1 is a table with two rows corresponding to the unique values in Gender. The GroupCount column shows the number of observations in each group. The columns mean_Age, mean_Weight, and mean_Smoker show the means of Age, Weight, and Smoker grouped by Gender.

Compute the mean for Age and Weight grouped by the values in Smoker. Specify Age and Weight as the variables for which you want to compute summary statistics by using the DataVars name-value argument. You must use DataVars because the input tbl includes the Gender variable, which is a cell array, and the built-in summary statistic mean is valid only for numeric and logical arrays.

tblstats2 = grpstats(tbl,"Smoker","mean","DataVars",["Age","Weight"])
tblstats2=2×4 table
Smoker    GroupCount    mean_Age    mean_Weight
______    __________    ________    ___________

0    false         66          37.97       149.91
1    true          34         38.882       161.94

Compute the minimum and maximum weight grouped by the combinations of values for Gender and Smoker.

tblstats3 = grpstats(tbl,["Gender","Smoker"],["min","max"], ...
"DataVars","Weight")
tblstats3=4×5 table
Gender      Smoker    GroupCount    min_Weight    max_Weight
__________    ______    __________    __________    __________

Male_0      {'Male'  }    false         26           158           194
Male_1      {'Male'  }    true          21           164           202
Female_0    {'Female'}    false         40           111           147
Female_1    {'Female'}    true          13           115           146

Smoker and Gender each have two unique values, so the output table includes four rows for the possible combinations: Male Nonsmoker (Male_0), Male Smoker (Male_1), Female Nonsmoker (Female_0), and Female Smoker (Female_1).

Specify the names for the columns in the output by using the VarNames name-value argument.

tblstats4 = grpstats(tbl,["Gender","Smoker"],["min","max"], ...
"DataVars","Weight", ...
"VarNames",["Gender","Smoker","Group Count", ...
"Lowest Weight","Highest Weight"])
tblstats4=4×5 table
Gender      Smoker    Group Count    Lowest Weight    Highest Weight
__________    ______    ___________    _____________    ______________

Male_0      {'Male'  }    false         26              158              194
Male_1      {'Male'  }    true          21              164              202
Female_0    {'Female'}    false         40              111              147
Female_1    {'Female'}    true          13              115              146

Compute group means for input data in a matrix. Group the input data using one or two grouping variables.

Load the carsmall data set, which contains measurements of 100 cars.

Compute group means for the variable Acceleration grouped by the variables Origin and Cylinders. The variable Acceleration is the time from 0 to 60 MPH in seconds. The grouping variable Origin is the country of origin for each car (France, Germany, Italy, Japan, Sweden, or USA). The grouping variable Cylinders has three unique values, 4, 6, and 8, indicating the number of cylinders in each car.

Calculate the mean acceleration grouped by the country of origin.

means = grpstats(Acceleration,Origin)
means = 6×1

14.4377
18.0500
15.8867
16.3778
16.6000
15.5000

means is a 6-by-1 vector of mean accelerations, where each value corresponds to a country of origin.

Calculate the mean acceleration grouped by both the country of origin and number of cylinders. Return the group names along with the mean acceleration for each group.

[means,grps] = grpstats(Acceleration,{Origin,Cylinders}, ...
["mean","gname"])
means = 10×1

17.0818
16.5267
11.6406
18.0500
15.9143
15.5000
16.3375
16.7000
16.6000
15.5000

grps = 10x2 cell
{'USA'    }    {'4'}
{'USA'    }    {'6'}
{'USA'    }    {'8'}
{'France' }    {'4'}
{'Japan'  }    {'4'}
{'Japan'  }    {'6'}
{'Germany'}    {'4'}
{'Germany'}    {'6'}
{'Sweden' }    {'4'}
{'Italy'  }    {'4'}

The two grouping variables Origin and Cylinders have 18 possible combinations because Origin has six unique values and Cylinders has three unique values. Only 10 of the possible combinations appear in the data, so means is a 10-by-1 vector of group means corresponding to the observed combinations of values. The output grps shows the 10 observed combinations of grouping variable values. For example, the mean acceleration of 4-cylinder cars made in France is 18.05.

Compute multiple group summary statistics for input data in a matrix.

Load the carsmall data set, which contains measurements of 100 cars.

Compute group summary statistics for the variable Acceleration grouped by the variable Origin. The variable Acceleration is the time from 0 to 60 MPH in seconds, and the grouping variable Origin is the country of origin for each car (France, Germany, Italy, Japan, Sweden, or USA).

Return the minimum and maximum acceleration grouped by the country of origin.

[grpMin,grpMax,grp] = grpstats(Acceleration,Origin, ...
["min","max","gname"])
grpMin = 6×1

8.0000
15.3000
13.9000
12.2000
15.7000
15.5000

grpMax = 6×1

22.2000
21.9000
18.2000
24.6000
17.5000
15.5000

grp = 6x1 cell
{'USA'    }
{'France' }
{'Japan'  }
{'Germany'}
{'Sweden' }
{'Italy'  }

The car with the lowest acceleration is made in the USA, and the car with the highest acceleration is made in Germany.

Compute summary statistics for input data in a table. Pass in [] for the grouping variable so that grpstats computes summary statistics without grouping.

Create a table that contains the variables Age, Weight, and Smoker.

tbl = table(Age,Weight,Smoker);

The variables Age and Weight have numeric values, and Smoker has logical values.

Compute the mean, minimum, and maximum for the numeric arrays Age and Weight and the logical array Smoker, with no grouping.

tblstats = grpstats(tbl,[],["mean","min","max"])
tblstats=1×10 table
GroupCount    mean_Age    min_Age    max_Age    mean_Weight    min_Weight    max_Weight    mean_Smoker    min_Smoker    max_Smoker
__________    ________    _______    _______    ___________    __________    __________    ___________    __________    __________

All       100         38.28        25         50           154           111           202           0.34          false         true

The observation name All indicates that grpstats uses all observations in tbl to compute the summary statistics.

Compute and plot means and prediction intervals for each group of input data in a matrix.

Load the carsmall data set, which contains measurements of 100 cars.

Compute group summary statistics for the variable Weight grouped by the variable Model_Year. The variable Weight contains car weight values, and the grouping variable Model_Year has three unique values, 70, 76, and 82, which correspond to the model years 1970, 1976, and 1982.

Calculate the mean weight and 90% prediction intervals for each model year.

[means,pred,grp] = grpstats(Weight,Model_Year, ...
["mean","predci","gname"],"Alpha",0.1);

Plot error bars showing the mean weight and 90% prediction intervals grouped by model year. Specify the horizontal tick labels as the group names.

f = figure;
ngrps = length(grp); % Number of groups
errorbar((1:ngrps)',means,pred(:,2)-means)
xlim([0.5 3.5])
f.CurrentAxes.XTick = 1:ngrps;
f.CurrentAxes.XTickLabel = grp;
title("90% Prediction Intervals for Weight by Year")
xlabel("Year")
ylabel("Weight")

Plot group means and confidence intervals for input data in a matrix. Group the input data using one or two grouping variables, and specify one or two variables for which you want to plot the summary statistics.

Load the carsmall data set, which contains measurements of 100 cars.

The variable Acceleration is the time from 0 to 60 MPH in seconds. The grouping variable Cylinders is the number of cylinders in each car.

Plot the mean acceleration grouped by cylinder, with 95% confidence intervals.

grpstats(Acceleration,Cylinders,0.05);
legend("Acceleration")

The mean acceleration for cars with 8 cylinders is significantly lower than for cars with 4 or 6 cylinders.

The variable Weight is the weight value for each car. Plot the mean acceleration and weight grouped by cylinder, with 95% confidence intervals. Scale the Weight values by 1000 so the means of Weight and Acceleration are the same order of magnitude.

grpstats([Acceleration,Weight/1000],Cylinders,0.05);
legend("Acceleration","Weight/1000")

The mean weight of cars increases with the number of cylinders, and the mean acceleration decreases with the number of cylinders.

The Model_Year variable has three unique values, 70, 76, and 82, which correspond to the model years 1970, 1976, and 1982. Plot the mean acceleration grouped by both cylinder and model year. Specify 95% confidence intervals.

grpstats(Acceleration,{Cylinders,Model_Year},0.05);
legend("Acceleration")

The two grouping variables Cylinders and Model_Year have nine possible combinations of values, because each variable has three unique values. The plot does not show 8-cylinder cars with the model year 1982 because the data does not include this combination.

The mean acceleration of 8-cylinder cars made in 1976 is significantly larger than the mean acceleration of 8-cylinder cars made in 1970.

Define a custom summary statistic by using an anonymous function. Pass the anonymous function to grpstats to compute the custom summary statistic for each group of input data.

Create a table that contains the variables Age, Smoker, and LastName.

tbl = table(Age,Smoker,LastName);

Find the number of smokers for each age group by using a custom function that computes the sum of each column of an input matrix.

f_sum = @(x)sum(x,1);
tblstats1 = grpstats(tbl,"Age",f_sum,"DataVars","Smoker", ...
"VarNames",["Age","Group Count","Number of Smokers"])
tblstats1=25×3 table
Age    Group Count    Number of Smokers
___    ___________    _________________

25    25          6                 1
27    27          1                 1
28    28          5                 2
29    29          3                 0
30    30          4                 1
31    31          4                 2
32    32          4                 1
33    33          3                 3
34    34          1                 0
35    35          2                 0
36    36          4                 0
37    37          5                 2
38    38          6                 2
39    39          8                 3
40    40          4                 1
41    41          3                 0
⋮

tblstats1 is a table with 25 rows corresponding to the unique values in Age. The Group Count column shows the number of observations in each age group, and the last column shows the number of smokers in each group.

Determine the mean length of the last name for each age group by using a custom function that computes the mean length of the elements in a cell array.

f_length = @(x)mean(cellfun("length",x));
tblstats2 = grpstats(tbl,"Age",f_length,"DataVars","LastName", ...
"VarNames",["Age","Group Count","Mean Length of Last Name"])
tblstats2=25×3 table
Age    Group Count    Mean Length of Last Name
___    ___________    ________________________

25    25          6                  5.6667
27    27          1                       6
28    28          5                     5.4
29    29          3                  5.6667
30    30          4                     6.5
31    31          4                    5.25
32    32          4                     6.5
33    33          3                  6.3333
34    34          1                       9
35    35          2                     7.5
36    36          4                    6.25
37    37          5                     8.2
38    38          6                  5.8333
39    39          8                   6.125
40    40          4                     5.5
41    41          3                  5.3333
⋮

## Input Arguments

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Input data, specified as a table. tbl must include at least one grouping variable, which you specify using groupvars. You can select variables for which to calculate summary statistics by using the DataVars name-value argument.

Each variable in tbl can be a numeric, logical, categorical, datetime, duration, or calendar duration vector, a character or string array, or a cell array of character vectors. You cannot specify a calendar duration vector as a grouping variable.

Identifiers for the grouping variables in the table input tbl, specified as one of the values in this table.

ValueDescription
Character vector, string array, or cell array of character vectorsNames of the grouping variables
Vector of positive integersVariable numbers of the grouping variables
Vector of logical values with the number of elements equal to the number of variables in tblLogical indicator with the value true for grouping variables and false otherwise
[]No groups (returns summary statistics for all data)

The variables specified by groupvars as grouping variables must have a data type that is valid for grouping variables: numeric, logical, categorical, datetime, or duration vector; character or string array; or cell array of character vectors.

For example, consider an input table tbl with six variables. The fourth variable is named Gender. To specify the variable Gender as the grouping variable, you can use one of these syntaxes:

• tblstats = grpstats(tbl,"Gender")

• tblstats = grpstats(tbl,4)

• tblstats = grpstats(tbl,logical([0 0 0 1 0 0]))

Data Types: single | double | logical | char | string | cell

Types of summary statistics to compute, specified as one of the following values.

• Character vector or string scalar specifying the built-in summary statistic, as described in this table.

Built-in Summary StatisticDescription
"gname"Group name
"numel"Count, or number, of non-NaN elements

If you specify input data as a table tbl, then the output table tblstats includes the group name and group count by default. You do not need to specify "gname" and "numel".

For numeric and logical variables, you can also specify one of these built-in summary statistics.

Built-in Summary StatisticDescription
"mean"Mean
"sem"Standard error of the mean
"std"Standard deviation
"var"Variance
"min"Minimum
"max"Maximum
"range"Range
"meanci"95% confidence interval for the mean. You can specify different significance levels using the Alpha name-value argument.
"predci"95% prediction interval for a new observation. You can specify different significance levels using the Alpha name-value argument.

• Function handle to specify any other types of summary statistics. You can use the handle to any function that accepts a column or matrix of data, and returns the same size output each time grpstats calls the function handle (even if the output for some groups is empty).

• If the function accepts a column of data, then the function can return either a scalar value or an nvals-by-1 column vector for descriptive statistics of length nvals (for example, a confidence interval has length two). If the function accepts a matrix, the function must return either a 1-by-ncols row vector or an nvals-by-ncols matrix, where ncols is the number of columns in the input data matrix.

• For functions that do not compute column-wise statistics, specify the computation direction while specifying the function. For example, to use the sum function, specify the function handle as @(x)sum(x,1) because sum computes column-wise statistics for matrices with two or more rows, but not for single-row matrices.

• String array or a cell array of character vectors or function handles to specify multiple types of summary statistics.

Example: stat1 = grpstats(X,group,"sem")

Example: stat1 = grpstats(X,group,@(x)sum(x,1))

Example: [stat1,stat2,stat3] = grpstats(X,group,{"mean","std",@skewness})

Input data, specified as a vector or matrix. If X is a matrix, then grpstats returns summary statistics for each column of X.

Data Types: single | double | logical | char | string | cell | categorical | datetime | duration | calendarDuration

Grouping variables for the input array X, specified as a numeric, logical, categorical, datetime, or duration vector, a character or string array, a cell array of character vectors, or a cell array of multiple grouping variables.

grpstats groups data in X using the grouping variable values. Use [] to compute summary statistics for all data, without grouping.

You can also use more than one grouping variable to group data for summary statistics. In this case, specify a cell array of grouping variables.

For example, consider the two grouping variables Gender and Smoker. The variable Gender is a string array with the values "Male" and "Female", and the variable Smoker is a logical vector with the value 0 for nonsmokers and 1 for smokers. If you specify the cell array {Gender,Smoker}, then grpstats divides observations into four groups: Male Smoker, Male Nonsmoker, Female Smoker, and Female Nonsmoker. grpstats returns summary statistics only for the combinations of values that exist in the grouping variables (not all possible combinations).

Data Types: single | double | logical | char | string | cell | categorical | datetime | duration

Significance level for plotting, specified as a scalar value in the range (0,1).

Use the syntax grpstats(X,group,alpha) to plot group means and corresponding 100×(1 – alpha)% confidence intervals.

Data Types: double

### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: "DataVars",[1,3,4],"Alpha",0.01 calculates summary statistics for the 1st, 3rd, and 4th variables in the input table, with 99% confidence intervals.

Significance level for confidence and prediction intervals, specified as a scalar value in the range (0,1).

When you include "meanci" or "predci" in whichstats, you can use Alpha to specify the significance level for confidence or prediction intervals, respectively. If you specify the value α, then grpstats returns 100×(1 – α)% confidence or prediction intervals. If you do not specify a value for Alpha, then grpstats returns 95% intervals (α = 0.05).

Example: "Alpha",0.1

Data Types: double

Table variables in tbl for which to compute summary statistics, specified as one of the values in this table.

ValueDescription
Character vector, string array, or cell array of character vectorsNames of the table variables
Vector of positive integersVariable numbers of the table variables in tbl
Vector of logical values with the number of elements equal to the number of variables in tblLogical indicator with the value true to include the table variables and false otherwise

Example: "DataVars",["Height","Weight"]

Data Types: double | string | cell | char

Variable (column) names for the output table tblstats, specified as a string array or a cell array of character vectors. By default, grpstats constructs output variable names by appending a prefix to them from the input data tbl. This prefix corresponds to the summary statistic name.

Example: "VarNames",["Gender","GroupCount","MaleMean","FemaleMean"]

Data Types: string | cell

## Output Arguments

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Group summary statistics for the table input tbl, returned as a table.

tblstats contains a row for each observed unique value or combination of values in the grouping variables, and includes columns for the following:

• All grouping variables specified by groupvars

• The variable GroupCount, which contains the number of observations in each group

• Group summary statistic values for all variables in tbl (other than the grouping variables) or for only the variables specified by DataVars

The total number of columns in tblstats is ngroupvars + 1 + ndatavars×nstats, where ngroupvars is the number of observed unique values or combinations of values in groupvars, ndatavars is the number of variables for which summary statistics are computed, and nstats is the number of summary statistic types specified in whichstats.

grpstats assigns default names to the columns in tblstats unless you specify column names using the name-value argument VarNames.

Group summary statistic values for the matrix input X, returned as an ngroups-by-ncols array. Here, ngroups is the number of observed unique values or combinations of values in the grouping variables specified in group, and ncols is the number of columns in X. Each column of stats contains the summary statistics for the corresponding column of X.

If X is a numeric or logical matrix, then the summary statistic is the mean of each group. Otherwise, the summary statistic is the number of elements in each group.

Multiple group summary statistics for the matrix input X, returned as ngroups-by-ncols arrays. Here, ngroups is the number of observed unique values or combinations of values in the grouping variables specified in group, and ncols is the number of columns in X. Each column of the output array contains the summary statistics for the corresponding column of X.

You must specify an output argument for each type of summary statistic specified in whichstats.

If a summary statistic type in whichstats returns a value of length nvals (for example, a confidence interval is a descriptive statistic of length two), then the corresponding output argument is an ngroups-by-ncols-by-nvals array.

## Algorithms

• grpstats computes summary statistic values for each observed unique value or combination of values in the grouping variables.

• If you specify a single grouping variable, then the output of grpstats contains a row for each observed unique value of the grouping variable. grpstats sorts the groups by order of appearance (if the grouping variable is a character vector or string scalar); in ascending numeric order (if the grouping variable is numeric); or in order of by category (if the grouping variable is categorical).

• If you specify multiple grouping variables, then the output of grpstats contains a row for each observed unique combination of values in the grouping variables. For example, if you specify two grouping variables, each with two values, then the output has four possible combinations of grouping variable values. The function computes summary statistics only for the observed combinations that exist in the input grouping variables (not all possible combinations). grpstats sorts the groups by the values of the first grouping variable, then the second grouping variable, and so on.

• grpstats ignores missing values in tbl, X, and group. Missing values depend on the data type:

• NaN for double, single, duration, and calendarDuration

• NaT for datetime

• <missing> for string

• <undefined> for categorical

• ' ' for char

• {''} for cell of character vectors

## Alternative Functionality

MATLAB® includes the function groupsummary, which also returns group summaries and is recommended when you are working with a table. groupsummary allows you to specify whether to include groups that consist of missing values and groups with zero elements in the output. Also, the function supports various group binning schemes and anonymous functions that require more than one input argument for custom summary statistics.

## Version History

Introduced before R2006a