$d_s$ for Between Subjects with Pooled SD Denominator

This function displays d for two between subjects groups and gives the central and non-central confidence interval using the pooled standard deviation as the denominator.

Usage

calculate_d(
  m1 = NULL,
  m2 = NULL,
  sd1 = NULL,
  sd2 = NULL,
  n1 = NULL,
  n2 = NULL,
  t = NULL,
  model = NULL,
  df = NULL,
  x_col = NULL,
  y_col = NULL,
  d = NULL,
  a = 0.05,
  lower = TRUE
)

Arguments

m1: mean group one
m2: mean group two
sd1: standard deviation group one
sd2: standard deviation group two
n1: sample size group one
n2: sample size group two
t: optional, calculate d from independent t, you must include n1 and n2 for degrees of freedom
model: optional, calculate d from t.test for independent t, you must still include n1 and n2
df: optional dataframe that includes the x_col and y_col
x_col: name of the column that contains the factor levels OR a numeric vector of group 1 scores
y_col: name of the column that contains the dependent score OR a numeric vector of group 2 scores
d: a previously calculated d value from a study
a: significance level
lower: Use this to indicate if you want the lower or upper bound of d for one sided confidence intervals. If d is positive, you generally want lower = TRUE, while negative d values should enter lower = FALSE for the upper bound that is closer to zero.

Value

Provides the effect size (Cohen's *d*) with associated central and non-central confidence intervals, the *t*-statistic, the confidence intervals associated with the means of each group, as well as the standard deviations and standard errors of the means for each group. The one-tailed confidence interval is also included for sensitivity analyses.

d: effect size
dlow: noncentral lower level confidence interval of d value
dhigh: noncentral upper level confidence interval of d value
dlow_central: central lower level confidence interval of d value
dhigh_central: central upper level confidence interval of d value
done_low: noncentral lower bound of one tailed confidence interval
done_low_central: central lower bound of one tailed confidence interval
M1: mean of group one
sd1: standard deviation of group one mean
se1: standard error of group one mean
M1low: lower level confidence interval of group one mean
M1high: upper level confidence interval of group one mean
M2: mean of group two
sd2: standard deviation of group two mean
se2: standard error of group two mean
M2low: lower level confidence interval of group two mean
M2high: upper level confidence interval of group two mean
spooled: pooled standard deviation
sepooled: pooled standard error
n1: sample size of group one
n2: sample size of group two
df: degrees of freedom (n1 - 1 + n2 - 1)
t: t-statistic
p: p-value
estimate: the d statistic and confidence interval in APA style for markdown printing
statistic: the t-statistic in APA style for markdown printing

Details

To calculate $d_s$, mean two is subtracted from mean one and divided by the pooled standard deviation. $$d_s = \frac{M_1 - M_2}{S_{pooled}}$$

You should provide one combination of the following:

1: m1 through n2

2: t, n1, n2

3: model, n1, n2

4: df, "x_col", "y_col"

5: x_col, y_col as numeric vectors

6: d, n1, n2

You must provide alpha and lower to ensure the right confidence interval is provided for you.

Examples

calculate_d(m1 = 14.37, # neglect mean
   sd1 = 10.716, # neglect sd
   n1 = 71, # neglect n
   m2 = 10.69, # none mean
   sd2 = 8.219, # none sd
   n2 = 3653, # none n
   a = .05, # alpha/confidence interval
   lower = TRUE) # lower or upper bound
#> $d
#> [1] 0.4448249
#> 
#> $dlow
#> [1] 0.2097233
#> 
#> $dhigh
#> [1] 0.6798669
#> 
#> $dlow_central
#> [1] 0.2096767
#> 
#> $dhigh_central
#> [1] 0.6799731
#> 
#> $done_low
#> [1] 0.2475166
#> 
#> $done_low_central
#> [1] 0.2474974
#> 
#> $M1
#> [1] 14.37
#> 
#> $sd1
#> [1] 10.716
#> 
#> $se1
#> [1] 1.271755
#> 
#> $M1low
#> [1] 11.83356
#> 
#> $M1high
#> [1] 16.90644
#> 
#> $M2
#> [1] 10.69
#> 
#> $sd2
#> [1] 8.219
#> 
#> $se2
#> [1] 0.135986
#> 
#> $M2low
#> [1] 10.42338
#> 
#> $M2high
#> [1] 10.95662
#> 
#> $spooled
#> [1] 8.272918
#> 
#> $sepooled
#> [1] 0.9913101
#> 
#> $n1
#> [1] 71
#> 
#> $n2
#> [1] 3653
#> 
#> $df
#> [1] 3722
#> 
#> $t
#> [1] 3.712259
#> 
#> $p
#> [1] 0.0002084243
#> 
#> $estimate
#> [1] "$d_s$ = 0.44, 95\\% CI [0.21, 0.68]"
#> 
#> $statistic
#> [1] "$t$(3722) = 3.71, $p$ < .001"
#>

\(d_s\) for Between Subjects with Pooled SD Denominator

Usage

Arguments

Value

Details

Examples