DMAR (version 1.0.0)

descriptives: Descriptive Statistics for One or More Variables

Description

Computes a compact set of descriptive statistics useful for data screening and psychometric work (including skewness and excess kurtosis), with an optional correlation matrix for the numeric variables.

Usage

descriptives(x, correlations = FALSE, listwise = FALSE)

Value

A list with two elements, returned in a stable shape regardless of the

correlations argument:

descriptives

A data.frame with one row per input variable and columns variable, type, n, n_missing, prop_missing, mean, median, sd, min, max, q25, q75, skewness, and kurtosis (excess kurtosis). For non-numeric variables, the numeric summary columns are NA.

correlations

A \(p \times p\) correlation matrix among the numeric variables, or NULL if correlations = FALSE or fewer than two numeric variables are available. This is returned as a plain matrix (not a table), because its natural structure is a symmetric two-dimensional array; that format reads well and plugs directly into downstream tools such as cov2cor or factor analysis and SEM software.

Arguments

x

A data.frame, tibble, or matrix containing the variables to summarize. A matrix is coerced to a data.frame.

correlations

Logical. If TRUE, also return a correlation matrix for the numeric variables (see Details).

listwise

Logical. If TRUE, apply listwise deletion (drop every row containing any NA) to x before computing any statistics. If FALSE (the default), each variable is summarized using its own available (non-missing) observations.

Author

Ken Kelley [email protected]

Details

Skewness and kurtosis. The reported values use the bias-corrected formulas commonly referred to as SAS/SPSS Type 2: $$\mathrm{skewness} = \frac{n}{(n-1)(n-2)} \sum_{i=1}^{n} \left(\frac{x_i - \bar{x}}{s}\right)^3,$$ $$\mathrm{kurtosis} = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \sum_{i=1}^{n} \left(\frac{x_i - \bar{x}}{s}\right)^4 - \frac{3(n-1)^2}{(n-2)(n-3)},$$ where \(s\) is the (divisor-\(n-1\)) sample standard deviation. Kurtosis is reported as excess kurtosis, so a normal distribution has an expected value of 0. As a rough guide to deciding whether normal-theory inference (e.g., maximum likelihood in factor analysis or SEM) is defensible, values of \(|\mathrm{skewness}| > 2\) or \(|\mathrm{kurtosis}| > 7\) are frequently flagged as problematic.

Variable-type handling. Each column is classified as "numeric", "integer", "logical", "factor", "character", or whatever its first class is otherwise. Columns of type "numeric", "integer", and "logical" receive full distributional summaries (logicals are coerced so that mean is the proportion of TRUEs). All other columns report only n, n_missing, and prop_missing; their remaining columns are NA.

Correlations. The correlation matrix, when requested, uses Pearson correlations with use = "pairwise.complete.obs" so that each pairwise correlation uses the maximum information available. Only numeric-type variables are included.

See Also

cor, quantile

Other descriptive statistics: kurtosis(), skewness()

Examples

# Four cognitive tests from the Holzinger and Swineford (1939) study
# (301 children in two schools).
hs_tests <- holzinger_swineford[, c("t1_visual_perception", "t2_cubes",
                                    "t4_lozenges",
                                    "t6_paragraph_comprehension")]
descriptives(hs_tests)

# Include a correlation matrix (useful during scale development).
descriptives(hs_tests, correlations = TRUE)

# Mixed-type data: numeric summaries for the test scores, and
# type = "factor" (with NA numeric columns) for school.
descriptives(holzinger_swineford[, c("school", "t1_visual_perception",
                                     "t2_cubes")])

# Data with missing values: the revised paper form board and flags tests
# were administered only in the Grant-White school, so 156 of the 301
# children have no score. Per-variable N and missingness are reported.
hs_partial <- holzinger_swineford[, c("t1_visual_perception",
                                      "t25_paper_form_board_r",
                                      "t26_flags")]
descriptives(hs_partial)

# The same data with listwise deletion applied first.
descriptives(hs_partial, listwise = TRUE)