mean_change: Mean Change Across Two Timepoints (dependent two-samples t-test)

Description

mean_change tests for mean change across two timepoints with a dependent two-samples t-test. The function also calculates the descriptive statistics for the timepoints and the standardized mean difference (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). mean_change is simply a wrapper for t.test plus some extra calculations.

Usage

mean_change(
  pre,
  post,
  standardizer = "pre",
  d.ci.type = "unbiased",
  ci.level = 0.95,
  check = TRUE
)

Value

list of numeric vectors containing statistical information about the mean change: 1) nhst = dependent two-samples t-test stat info in a numeric vector, 2) desc = descriptive statistics stat info in a numeric vector, 3) std = standardized mean difference stat info in a numeric vector

1) nhst = dependent two-samples t-test stat info in a numeric vector

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

standard error

t-value

degrees of freedom

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 numeric vector

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

sample size of the change score

Pearson correlation between the pre and post variables

3) std = standardized mean difference stat info in a numeric vector

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

Arguments

pre: numeric vector of the variable at the pre-timepoint.
post: numeric vector of the variable at the post-timepoint. The elements must correspond to the same cases in pre as pairs by position. Thus, the length of post must be the same as pre. Note, missing values in post are expected and handled with listwise deletion.
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 interval (and standard error) of the standardized mean difference. 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 post is the same length as pre. This is a tradeoff between computational efficiency (FALSE) and more useful error messages (TRUE).

Details

mean_change calculates the mean change as 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 was y in t.test(paired = TRUE).

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.

Examples

Run this code


# dependent two-sample t-test
mean_change(pre = mtcars$"disp", post = mtcars$"hp") # standardizer = "pre"
mean_change(pre = mtcars$"disp", post = mtcars$"hp", d.ci.type = "classic")
mean_change(pre = mtcars$"disp", post = mtcars$"hp", standardizer = "pooled")
mean_change(pre = mtcars$"disp", post = mtcars$"hp", ci.level = 0.99)
mean_change(pre = mtcars$"hp", post = mtcars$"disp",
   ci.level = 0.99) # note, when flipping pre and post, the cohen's d estimate
   # changes with standardizer = "pre" because the "pre" variable is different.
   # This does not happen for standardizer = "pooled" or "change". For example...
mean_change(pre = mtcars$"disp", post = mtcars$"hp", standardizer = "pooled")
mean_change(pre = mtcars$"hp", post = mtcars$"disp", standardizer = "pooled")
mean_change(pre = mtcars$"disp", post = mtcars$"hp", standardizer = "change")
mean_change(pre = mtcars$"hp", post = mtcars$"disp", standardizer = "change")

# same as intercept-only regression with the change score
mean_change(pre = mtcars$"disp", post = mtcars$"hp")
lm_obj <- lm(hp - disp ~ 1, data = mtcars)
coef(summary(lm_obj))

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