There are many summary statistics available in R; this function provides the ones most useful for scale construction and item analysis in classic psychometrics. Range is most useful for the first pass in a data set, to check for coding errors.

```
describe(x, na.rm = TRUE, interp=FALSE,skew = TRUE, ranges = TRUE,trim=.1,
type=3,check=TRUE,fast=NULL,quant=NULL,IQR=FALSE,omit=FALSE,data=NULL)
describeData(x,head=4,tail=4)
describeFast(x)
```

x

A data frame or matrix

na.rm

The default is to delete missing data. na.rm=FALSE will delete the case.

interp

Should the median be standard or interpolated

skew

Should the skew and kurtosis be calculated?

ranges

Should the range be calculated?

trim

trim=.1 -- trim means by dropping the top and bottom trim fraction

type

Which estimate of skew and kurtosis should be used? (See details.)

check

Should we check for non-numeric variables? Slower but helpful.

fast

if TRUE, will do n, means, sds, min, max, ranges for an improvement in speed. If NULL, will switch to fast mode for large (ncol * nrow > 10^7) problems, otherwise defaults to fast = FALSE

quant

if not NULL, will find the specified quantiles (e.g. quant=c(.25,.75) will find the 25th and 75th percentiles)

IQR

If TRUE, show the interquartile range

omit

Do not convert non-numerical variables to numeric, omit them instead

head

show the first 1:head cases for each variable in describeData

tail

Show the last nobs-tail cases for each variable in describeData

data

Allows formula input for specific grouping variables

A data.frame of the relevant statistics: item name item number number of valid cases mean standard deviation trimmed mean (with trim defaulting to .1) median (standard or interpolated mad: median absolute deviation (from the median). minimum maximum skew kurtosis standard error

In basic data analysis it is vital to get basic descriptive statistics.
Procedures such as `summary`

and Hmisc::describe do so. The describe function in the `psych`

package is meant to produce the most frequently requested stats in psychometric and psychology studies, and to produce them in an easy to read data.frame. If a grouping variable is called for in formula mode, it will also call `describeBy`

to the processing. The results from describe can be used in graphics functions (e.g., `error.crosses`

).

The range statistics (min, max, range) are most useful for data checking to detect coding errors, and should be found in early analyses of the data.

Although describe will work on data frames as well as matrices, it is important to realize that for data frames, descriptive statistics will be reported only for those variables where this makes sense (i.e., not for alphanumeric data).

If the check option is TRUE, variables that are categorical or logical are converted to numeric and then described. These variables are marked with an * in the row name. This is somewhat slower. Note that in the case of categories or factors, the numerical ordering is not necessarily the one expected. For instance, if education is coded "high school", "some college" , "finished college", then the default coding will lead to these as values of 2, 3, 1. Thus, statistics for those variables marked with * should be interpreted cautiously (if at all).

In a typical study, one might read the data in from the clipboard (`read.clipboard`

), show the splom plot of the correlations (`pairs.panels`

), and then describe the data.

na.rm=FALSE is equivalent to describe(na.omit(x))

When finding the skew and the kurtosis, there are three different options available. These match the choices available in skewness and kurtosis found in the e1071 package (see Joanes and Gill (1998) for the advantages of each one).

If we define \(m_r = [\sum(X- mx)^r]/n\) then

Type 1 finds skewness and kurtosis by \(g_1 = m_3/(m_2)^{3/2} \) and \(g_2 = m_4/(m_2)^2 -3\).

Type 2 is \(G1 = g1 * \sqrt{n *(n-1)}/(n-2)\) and \(G2 = (n-1)*[(n+1)g2 +6]/((n-2)(n-3))\).

Type 3 is \(b1 = [(n-1)/n]^{3/2} m_3/m_2^{3/2}\) and \(b2 = [(n-1)/n]^{3/2} m_4/m_2^2)\).

The additional helper function `describeData`

just scans the data array and reports on whether the data are all numerical, logical/factorial, or categorical. This is a useful check to run if trying to get descriptive statistics on very large data sets where to improve the speed, the check option is FALSE.

An even faster overview of the data is `describeFast`

which reports the number of total cases, number of complete cases, number of numeric variables and the number which are factors.

The fast=TRUE option will lead to a speed up of about 50% for larger problems by not finding all of the statistics (see NOTE)

To describe the data for different groups, see `describeBy`

or specify the grouping variable(s) in formula mode (see the examples).

Joanes, D.N. and Gill, C.A (1998). Comparing measures of sample skewness and kurtosis. The Statistician, 47, 183-189.

`describeBy`

, `skew`

, `kurtosi`

`interp.median`

, `read.clipboard`

. Then, for graphic output, see `error.crosses`

, `pairs.panels`

, `error.bars`

, `error.bars.by`

and `densityBy`

, or `violinBy`

# NOT RUN { data(sat.act) describe(sat.act) describe(sat.act ~ gender) #formula mode option calls describeBy for the entire data frame describe(SATV + SATQ ~ gender, data=sat.act) #formula mode specifies just two variables describe(sat.act,skew=FALSE) describe(sat.act,IQR=TRUE) #show the interquartile Range describe(sat.act,quant=c(.1,.25,.5,.75,.90) ) #find the 10th, 25th, 50th, #75th and 90th percentiles describeData(sat.act) #the fast version just gives counts and head and tail print(describeFast(sat.act),short=FALSE) #even faster is just counts (just less information) #now show how to adjust the displayed number of digits des <- describe(sat.act) #find the descriptive statistics. Keep the original accuracy des #show the normal output, which is rounded to 2 decimals print(des,digits=3) #show the output, but round to 3 (trailing) digits print(des, signif=3) #round all numbers to the 3 significant digits # }