psych (version 2.1.9)

# interp.median: Find the interpolated sample median, quartiles, or specific quantiles for a vector, matrix, or data frame

## Description

For data with a limited number of response categories (e.g., attitude items), it is useful treat each response category as range with width, w and linearly interpolate the median, quartiles, or any quantile value within the median response.

## Usage

```interp.median(x, w = 1,na.rm=TRUE)
interp.quantiles(x, q = .5, w = 1,na.rm=TRUE)
interp.quartiles(x,w=1,na.rm=TRUE)
interp.boxplot(x,w=1,na.rm=TRUE)
interp.values(x,w=1,na.rm=TRUE)
interp.qplot.by(y,x,w=1,na.rm=TRUE,xlab="group",ylab="dependent",

## Arguments

x

input vector

q

quantile to estimate ( 0 < q < 1

w

category width

y

input vector for interp.qplot.by

na.rm

should missing values be removed

xlab

x label

ylab

Y label

ylim

limits for the y axis

arrow.len

length of arrow in interp.qplot.by

typ

plot type in interp.qplot.by

...

## Value

im

interpolated median(quantile)

v

interpolated values for all data points

## Details

If the total number of responses is N, with median, M, and the number of responses at the median value, Nm >1, and Nb= the number of responses less than the median, then with the assumption that the responses are distributed uniformly within the category, the interpolated median is M - .5w + w*(N/2 - Nb)/Nm.

The generalization to 1st, 2nd and 3rd quartiles as well as the general quantiles is straightforward.

A somewhat different generalization allows for graphic presentation of the difference between interpolated and non-interpolated points. This uses the interp.values function.

If the input is a matrix or data frame, quantiles are reported for each variable.

`median`

## Examples

Run this code
``````# NOT RUN {
interp.median(c(1,2,3,3,3))  # compare with median = 3
interp.median(c(1,2,2,5))
interp.quantiles(c(1,2,2,5),.25)
x <- sample(10,100,TRUE)
interp.quartiles(x)
#
x <-  c(1,1,2,2,2,3,3,3,3,4,5,1,1,1,2,2,3,3,3,3,4,5,1,1,1,2,2,3,3,3,3,4,2)
y <-  c(1,2,3,3,3,3,4,4,4,4,4,1,2,3,3,3,3,4,4,4,4,5,1,5,3,3,3,3,4,4,4,4,4)
x <-  x[order(x)]   #sort the data by ascending order to make it clearer
y <- y[order(y)]
xv <- interp.values(x)
yv <- interp.values(y)
barplot(x,space=0,xlab="ordinal position",ylab="value")
lines(1:length(x)-.5,xv)
points(c(length(x)/4,length(x)/2,3*length(x)/4),interp.quartiles(x))
barplot(y,space=0,xlab="ordinal position",ylab="value")
lines(1:length(y)-.5,yv)
points(c(length(y)/4,length(y)/2,3*length(y)/4),interp.quartiles(y))
data(psychTools::galton)
galton <- psychTools::galton
interp.median(galton)
interp.qplot.by(galton\$child,galton\$parent,ylab="child height"
,xlab="Mid parent height")

# }
``````

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