tt: 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 analysis of the mean of a single variable or the independent groups analysis of the mean difference, from either data or summary statistics. This output includes the basic descriptive statistics, analysis of assumptions and the hypothesis test and confidence interval. For two groups the output also includes the pooled or within-group standard deviation, and the standardized mean difference or Cohen's d and its confidence interval. The output from data for two groups 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

tt(x=NULL, y=NULL, dframe=mydata, ...)
## S3 method for class 'brief':
tt(\ldots, brief=TRUE)
## S3 method for class 'default':
tt(x, y, 
         n = NULL, m = NULL, s = NULL, mu0 = NULL, 
         n1 = NULL, n2 = NULL,  m1 = NULL, m2 = NULL, s1 = NULL, s2 = NULL, 
         Ynm = "Y", Xnm = "X", X1nm = "Group1", X2nm = "Group2", 
         brief=FALSE, digits.d = NULL, 
         conf.level = 0.95, mmd = NULL, msmd = NULL, 
         bw1 = "nrd", bw2 = "nrd", \dots)
## S3 method for class 'formula':
tt(my.formula, y=NULL, dframe=mydata, \dots)
smd.t.test(...)
ttest(...)

Arguments

A formula, or the values of response variable for first group.

If x is not a formula, values of response variable for second group, otherwise NULL.

Sample size for one group.

mu0

Hypothesized mean for one group. If not present, then confidence interval only.

Sample size for first of two groups.

Sample size for second of two groups.

Sample mean for first of two groups.

Sample mean for second of two groups.

Sample standard deviation for first of two groups.

Sample standard deviation for second of two groups.

my.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.

dframe

Data frame that contains the variable of interest, default is mydata.

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.

brief

Extent of displayed results.

digits.d

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

conf.level

Confidence level of the interval, expressed as a proportion.

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

If n or n1 are set to values, then the analysis proceeds from the summary statistics, the sample size and mean and standard deviation of each group. Missing data are counted and then removed for further analysis of the non-missing data values. Otherwise the analysis proceeds from the data, which can be in a data frame with a grouping variable and response variable, or in two data vectors, one for each group.

Following the format and syntax of the standard t.test function, the methods for the generic function tt include 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. The vectors must be defined in the user workspace as they are generally of unequal length and so generally not conformable to a data frame. 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.

The formula version assumes the data are in a data frame. The input data frame has the assumed name of mydata. If this data frame is named something different, then specify the name with the dframe option. Regardless of its name, the data frame need not be attached to reference the variable directly by its name without having to invoke the mydata$name notation. The split version of the response variable, that is, its values organized into two vectors, one for each group, are saved in the global environment under the names group1 and group2 for further analysis if desired.

This version of tt 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.

If computed from the data, 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, when computed from the data 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 confidence interval of the standardized mean difference is computed by the ci.smd function, written by Ken Kelley, from the MBESS package.

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 tt, 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, ptt().

The number of decimal digits is determined by default from the largest number of decimal digits of the entered descriptive statistics. The number of decimal digits is then set at that value, plus one more. Or, override the default with the digits.d parameter.

A labels data frame named mylabels, obtained from the rad function, can list the label for some or all of the variables in the data frame that contains the data for the analysis. If this labels data frame exists, then the varible label for the response variable and the grouping variable is listed in the text output.

References

Kelley, K., smd function from the MBESS package.

Examples

Run this code

# ----------------------------------------------------------
# call tt with a formula
# ----------------------------------------------------------

# create simulated data, no population mean difference
# X has two values only, Y is numeric
# put into a data frame, required for formula version
n <- 12
X <- sample(c("Group1","Group2"), size=n, replace=TRUE)
Y <- rnorm(n=n, mean=50, sd=10)
mydata <- data.frame(X,Y)

# analyze data with formula version
# variable names and levels of X are automatically obtained from data
# although data frame is not attached, can reference the variable
#   names directly
tt(Y ~ X)
# brief version of results
tt.brief(Y ~ X)
# Compare to standard R function t.test
t.test(Y ~ X, var.equal=TRUE)

# consider the practical importance of the difference
tt(Y ~ X, msmd=.5)

# variable of interest is in a data frame which is not the default mydata
# access the data frame in the lessR dat.twogroup data set
# although data not attached, access the variables directly by their name
data(dat.twogroup)
tt(ShipTime ~ Supplier, dframe=dat.twogroup)


# ----------------------------------------------------------
# tt for a single group
# ----------------------------------------------------------

# confidence interval only, from data
tt(Y)

# confidence interval and hypothesis test, from data
tt(Y, mu0=52)

# confidence interval only, from descriptive stats
tt(n=34, m=8.92, s=1.67)

# confidence interval and hypothesis test, from descriptive stats
tt(n=34, m=8.92, s=1.67, mu0=9)


# -------------------------------------------------------
# tt from data stored in two vectors 
# -------------------------------------------------------

# create two separate vectors of response variable Y
# the vectors exist are not in a data frame
#   their lengths need not be equal
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
tt(Y1, Y2, Ynm="MyY", Xnm="MyX", X1nm="Group1", X2nm="Group2")


# -------------------------------------------------------
# analysis proceeds from summary statistics
# -------------------------------------------------------

# one group: sample size, mean and sd
# optional variable name added
tt(n=34, m=8.92, s=1.67, Ynm="Time")

# two groups: sample size, mean and sd for each group
# specify the briefer form of the output
tt.brief(n1=19, m1=9.57, s1=1.45, n2=15, m2=8.09, s2=1.59)

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