means_change {quest}

Mean Changes Across Two Timepoints For Multiple PrePost Pairs of Variables (dependent two-samples t-tests)

Description

means_change tests for mean changes across two timepoints for multiple prepost pairs of variables via dependent two-samples t-tests. The function also calculates the descriptive statistics for the timepoints and the standardized mean differences (i.e., Cohen's d) based on either the standard deviation of the pre-timepoint, pooled standard deviation of the pre-timepoint and post-timepoint, or the standard deviation of the change score (post - pre). means_change is simply a wrapper for t.test plus some extra calculations.

Usage

means_change(
  data,
  prepost.nm.list,
  standardizer = "pre",
  d.ci.type = "unbiased",
  ci.level = 0.95,
  check = TRUE
)

Arguments

data

data.frame of data.

prepost.nm.list

list of length-2 character vectors specifying the colnames from data corresponding to the prepost pairs of variables. For each element of the list, the character vector should have length 2 where the first element corresponds to the pre-timepoint variable colname of that prepost pair and the second element corresponds to the post-timepoint variable colname of that prepost pair. The names of the list will be the rownames in the data.frames of the return object. See examples. prepost.nm.list can also be a single length-2 character vector for the case of a single pre-post pair of variables, which is functionally equivalent to mean_change.

standardizer

chararacter vector of length 1 specifying what to use for standardization when computing the standardized mean difference (i.e., Cohen's d). There are three options: 1. "pre" for the standard deviation of the pre-timepoint, 2. "pooled" for the pooled standard deviation of the pre-timepoint and post-timepoint, 3. "change" for the standard deviation of the change score (post - pre). The default is "pre", which I believe makes the most theoretical sense (see Cumming, 2012); however, "change" is the traditional choice originally proposed by Jacob Cohen (Cohen, 1988).

d.ci.type

character vector of lenth 1 specifying how to compute the confidence intervals (and standard errors) of the standardized mean differences. There are currently two options: 1. "unbiased" which calculates the unbiased standard error of Cohen's d based on the formulas in Viechtbauer (2007). If standardizer = "pre" or "pooled", then equation 36 from Table 2 is used. If standardizer = "change", then equation 25 from Table 1 is used. A symmetrical confidence interval is then calculated based on the standard error. 2. "classic" which calculates the confidence interval of Cohen's d based on the confidence interval of the mean change itself. The lower and upper confidence bounds are divided by the standardizer. Technically, this confidence interval is biased due to not taking into account the uncertainty of the standardizer. No standard error is calculated for this option and NA is returned for "d_se" in the return object.

ci.level

double vector of length 1 specifying the confidence level. ci.level must range from 0 to 1.

check

logical vector of length 1 specifying whether the input arguments should be checked for errors. For example, checking whether prepost.nm.list is a list of length-2 character vectors. This is a tradeoff between computational efficiency (FALSE) and more useful error messages (TRUE).

Details

For each prepost pair of variables, means_change calculates the mean change as data[[ prepost.nm.list[[i]][2] ]] - data[[ prepost.nm.list[[i]][1] ]] (which corresponds to post - pre) such that increases over time have a positive mean change estimate and decreases over time have a negative mean change estimate. This would be as if the post-timepoint was x and the pre-timepoint y in t.test(paired = TRUE).

Value

list of data.frames containing statistical information about the mean change for each prepost pair of variables (the rownames of the data.frames are the names of prepost.nm.list): 1) nhst = dependent two-samples t-test stat info in a data.frame, 2) desc = descriptive statistics stat info in a data.frame, 3) std = standardized mean difference stat info in a data.frame,

1) nhst = dependent two-samples t-test stat info in a data.frame

est

mean change estimate (i.e., post - pre)

se

standard error

t

t-value

df

degrees of freedom

p

two-sided p-value

lwr

lower bound of the confidence interval

upr

upper bound of the confidence interval

2) desc = descriptive statistics stat info in a data.frame

mean_post

mean of the post variable

mean_pre

mean of the pre variable

sd_post

standard deviation of of the post variable

sd_pre

standard deviation of the pre variable

n

sample size of the change score

r

Pearson correlation between the pre and post variables

3) std = standardized mean difference stat info in a data.frame

d_est

Cohen's d estimate

d_se

Cohen's d standard error

d_lwr

Cohen's d lower bound of the confidence interval

d_upr

Cohen's d upper bound of the confidence interval

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences, 2nd ed. Hillsdale, NJ: Erlbaum.

Cumming, G. (2012). Understanding the new statistics: Effect sizes, confidence intervals, and meta-analysis. New York, NY: Rouledge.

Viechtbauer, W. (2007). Approximate confidence intervals for standardized effect sizes in the two-independent and two-dependent samples design. Journal of Educational and Behavioral Statistics, 32(1), 39-60.

See Also

mean_change for a single pair of prepost variables, t.test fixes the table of contents for some unknown reason, means_diff for multiple independent two-sample t-tests, means_test for multiple one-sample t-tests,

Examples

# dependent two-sample t-tests
prepost_nm_list <- list("first_pair" = c("disp","hp"), "second_pair" = c("carb","gear"))
means_change(mtcars, prepost.nm.list = prepost_nm_list)
means_change(mtcars, prepost.nm.list = prepost_nm_list, d.ci.type = "classic")
means_change(mtcars, prepost.nm.list = prepost_nm_list, standardizer = "change")
means_change(mtcars, prepost.nm.list = prepost_nm_list, ci.level = 0.99)

# same as intercept-only regression with the change score
means_change(data = mtcars, prepost.nm.list = c("disp","hp"))
lm_obj <- lm(hp - disp ~ 1, data = mtcars)
coef(summary(lm_obj))