lessR (version 1.5.2)

smd.t.test: Generic Method for t-test and Standardized Mean Difference with Enhanced Graphics

Description

Provides enhanced output from the standard t.test function applied to the independent groups analysis of the mean difference. This output includes the basic descriptive statistics, the pooled or within-group standard deviation, and the standardized mean difference or Cohen's d and its confidence interval, as well as an evaluation of assumptions. The output introduces the ODDSMD plot, which displays the Overlapping Density Distributions of the two groups as well as the means, mean difference and Standardized Mean Difference. The plot also includes the results of the descriptive and inferential analyses.

Usage

smd.t.test(x, ...)
## S3 method for class 'default':
smd.t.test(x, y, Ynm = "Y", Xnm = "X", 
       X1nm = "Group1", X2nm = "Group2", conf.level = 0.95, 
       mmd = NULL, msmd = NULL, digits = 2, 
       bw1 = "nrd", bw2 = "nrd", \dots)
## S3 method for class 'formula':
smd.t.test(formula, data, \dots)

Arguments

formula

A formula of the form Y ~ X, where Y is the numeric response variable compared across the two groups, and X is a grouping variable (factor) with two levels that define the corresponding groups.

data

An optional matrix or data frame containing the variables in the formula. By default the variables are taken from environment (formula).

conf.level

Confidence level of the interval, expressed as a proportion.

digits

Number of decimal places for which to display numeric values. Suggestion only.

x

Values of response variable for first group.

y

Values of response variable for second group.

Ynm

Name of response variable.

Xnm

Name of predictor variable, the grouping variable or factor with exactly two levels.

X1nm

Value of grouping variable, the level that defines the first group.

X2nm

Value of grouping variable, the level that defines the second group.

mmd

Minimum Mean Difference of practical importance, the difference of the response variable between two group means. The concept is optional, and only one of mmd and msmd is provided.

msmd

For the Standardized Mean Difference, Cohen's d, the Minimum value of practical importance. The concept is optional, and only one of mmd and msmd is provided.

bw1

Bandwidth for the computation of the densities for the first group.

bw2

Bandwidth for the computation of the densities for the second group.

...

Further arguments to be passed to or from methods.

Details

Following the format and syntax of the standard t.test function, the two methods for the generic function smd.t.test are formula and default. The formula method is invoked when the data include a variable that has exactly two values, a grouping variable or factor generically referred to as X, and a numerical response variable, generically referred to as Y. The formula is of the form Y ~ X, with the names Y and X replaced by the actual variable names specific to a particular analysis. The formula method automatically retrieves the names of the variables and data values for display on the resulting output.

The default method is invoked when the values of the response variable Y are organized into two vectors, the values of Y for each group in the corresponding vector. When submitting data in this form, the output is enhanced if the actual names of the variables referred to generically as X and Y, as well as the names of the levels of the factor X, are explicitly provided.

This version of smd.t.test assumes homogeneity of variance in the computation of the standard error of the mean difference. Also, only a two-sided test is provided. The null hypothesis is a population mean difference of 0.

The bandwidth parameter controls the smoothness of the estimated density curve. To obtain a smoother curve, increase the bandwidth from the default value.

For the output, the two groups are automatically arranged so that the group with the larger mean is listed as the first group. The result is that the resulting mean difference, as well as the standardized mean difference, is always non-negative.

The practical importance of the size of the mean difference is addressed when one of two parameter values are supplied, the minimum mean difference of practical importance, mmd, or the corresponding standardized version, msmd. The remaining value is calculated and both values are added to the graph and the console output.

After running smd.t.test, the following statistics are available for further analysis: sample sizes n1 and n2, sample means m1 and m2, sample standard deviations, s1 and s2, plus the within-group or pooled standard deviation, sw. For example, if the t-test does not achieve significance, then perhaps a power curve is of interest. Then n1, n2 and sw can be used to construct a power curve without re-entering their values, powercurve.t.test().

See Also

t.test, density, plot.density, powercurve.t.test, formula.

Examples

# ----------------------------------------------------------
# Data simulated, call smd.t.test with a formula
# ----------------------------------------------------------

# Create simulated data, no population mean difference
# X has two values only, Y is numeric
n <- 12
X <- sample(c("Group1","Group2"), size=n, replace=TRUE)
Y <- rnorm(n=n, mean=50, sd=10)

# Analyze data with formula version
# Variable names and levels of X are automatically obtained from data
smd.t.test(Y ~ X)

# Consider the practical importance of the difference
smd.t.test(Y ~ X, msmd=.5)


# -------------------------------------------------------
# Data stored in two vectors, call smd.t.test accordingly
# -------------------------------------------------------

# Create two separate vectors of response variable Y
n <- 10
Y1 <- rnorm(n=n/2, mean=50, sd=10)
Y2 <- rnorm(n=n/2, mean=60, sd=10)

# Analyze the two vectors directly
# Usually explicitly specify variable names and levels of X
#   to enhance the readability of the output
smd.t.test(Y1, Y2, Ynm="MyY", Xnm="MyX", X1nm="Group1", X2nm="Group2")