CI_mdiff_contrast_bs: Estimate the mean difference for an independent groups...

In rcalinjageman/esci2: Effect Sizes and Confidence Intervals

Description

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CI_mdiff_contrast_bs returns the point estimate and confidence interval for the mean difference in a linear contrast: \mjdeqn \psi = \sum_i=1^ac_iM_i psi = sum(contrasts*means) Where there are a groups, and M is each group mean and c is each group weight; see Kline, equation 7.1

Usage

CI_mdiff_contrast_bs(
  means,
  sds,
  ns,
  contrast,
  conf_level = 0.95,
  assume_equal_variance = FALSE
)

Arguments

means	A vector of 2 or more means
sds	A vector of standard deviations, same length as means
ns	A vector of sample sizes, same length as means
contrast	A vector of group weights, same length as means.
conf_level	The confidence level for the confidence interval in decimal form. Defaults to 0.95.
assume_equal_variance	Defaults to FALSE

Value

Returns a list with these named elements:

• effect_size - the point estimate from the sample

• lower - lower bound of the CI

• upper - upper bound of the CI

• df - degrees of freedom for the contrast

• se - standard error

• moe - margin of error

• variability_component - if equal variance is assumed, returns sd_pooled; otherwise returns sd_avg

This function only takes in summary data and provides only the minimal output. For a friendlier version of this function, see estimate_mdiff_contrast_bs

Details

With equal variance assumed:

If equal variance is assumed, the standard error is calculated as given in Kline, equation 7.8: \mjdeqn s_ \psi = \sqrtsd_pooled * (\sum_i=1^ac_i^2/n_i) s_psi = sd_pooled * sqrt(sum(contrast^2/ns)) where n is each group size and sd_pooled is the pooled standard deviation as given in Kline, equation 3.11: \mjdeqn sd_pooled = \frac \sum_i=1^a (n_i -1) s_i^2 \sum_i=1^a (n_i-1) sqrt(sum(variances*dfs) / sum(dfs))

where s is the standard deviation for each group.

Degrees of freedom for the analysis are calculated as given in Kline, equation 3.9: \mjdeqn df = \sum_i=1^an_i -1 sum(n-1)

Without assuming equal variance:

If equal variance is not assumed, the standard error is calculated as given in Baguley, equation 15.11: \mjdeqn s_ \psi = \sqrt \sum_i=1^a \frac c_i^2 s_i^2 n_i s_psi = sqrt(sum(contrast^2 * variances / ns))

The degrees of freedom for the analysis are calculated as in Baguley, equation 15.12: \mjdeqn df = \frac s_ \psi ^4 \sum_i=1^a \fracc_i^4 s_i^4 n_i^2 (n_i -1) se_psi^4 / sum( (contrast^4) * (sds^4) / (ns^2*dfs))

And the analysis also returns sd_avg, the square root of the average of the group variances, as given in Bonett, explanation of equation 6: \mjdeqn sd_avg = \sqrt \frac \sum_i=1^a s_i^2 a sqrt(mean(variances))

References

• Baguley, T. (2012). Serious Stats. In Serious stats: A guide to advanced statistics for the behavioral sciences. Macmillan Education UK. https://doi.org/10.1007/978-0-230-36355-7

• Bonett, D. G. (2018). R code posted to personal website. https://people.ucsc.edu/~dgbonett/psyc204.html

• Bonett, D. G. (2008). Confidence Intervals for Standardized Linear Contrasts of Means. Psychological Methods, 13(2), 99–109. https://doi.org/10.1037/1082-989X.13.2.99

• Kline, R. B. (2013). Beyond significance testing: Statistics reform in the behavioral sciences (2nd ed.). American Psychological Association. https://doi.org/10.1037/14136-000

See Also

• estimate_mdiff_contrast_bs for friendly version of this function

• CI_smd_contrast_bs to obtain a standardized mean difference

Examples

# Example from Kline, 2013
#  Data in Table 3.4
#  Worked out in Chapter 7
#  See note to table 7.2
# With equal variance assumed and no correction, should give:
#   psi = -2 95% CI [-5.23, 1.23]  (see note to Table 7.2)

CI_mdiff_contrast_bs(
  means = c(13, 11, 15),
  sds = c(2.738613, 2.236068, 2.000000),
  ns = c(5, 5, 5),
  contrast = contrast <- c(1, 0, -1),
  conf_level = 0.95,
  assume_equal_variance = TRUE
)

# Example from Kline, 2013
#  Data in Table 3.4
#  Worked out in Chapter 7
#  See note to table 7.2
# With equal variance assumed and no correction, should give:
#   psi = 3 95% CI [0.20, 5.80]  (see note to Table 7.2)

CI_mdiff_contrast_bs(
  means = c(13, 11, 15),
  sds = c(2.738613, 2.236068, 2.000000),
  ns = c(5, 5, 5),
  contrast = contrast <- c(1/2, -1, 1/2),
  conf_level = 0.95,
  assume_equal_variance = TRUE
)

# Example from Bonett, 2018, ci.lc.mean.bs, 
#  https://people.ucsc.edu/~dgbonett/psyc204.html
# Should give:
#                              Estimate       SE       df        LL        UL
# Equal Variances Assumed:        -5.35 1.300136 36.00000 -7.986797 -2.713203
# Equal Variances Not Assumed:    -5.35 1.300136 33.52169 -7.993583 -2.706417

CI_mdiff_contrast_bs(
  means = c(33.5, 37.9, 38.0, 44.1),
  sds = c(3.84, 3.84, 3.65, 4.98),
  ns = c(10,10,10,10),
  contrast = contrast <- c(.5, .5, -.5, -.5),
  conf_level = 0.95,
  assume_equal_variance = FALSE
)

rcalinjageman/esci2 documentation built on Dec. 22, 2021, 1:02 p.m.