PHattwosidedTestStatistics function

PHattwosidedTestStatistics

This function is a helper function for meta-analysis of experiments using PHat as an effect size. It returns the 100*(1-alpha/2)

PHattwosidedTestStatistics(
  effectsize,
  effectsize.variance,
  effectsize.df = 0,
  alpha = 0.05
)

Arguments

• effectsize: The overall estimate of the centralized PHat (ie.Phat-0.5) from a group of effect sizes to be meta-analysed
• effectsize.variance: The estimate of the variance of the overall estimate ofPHat
• effectsize.df: The total degrees of freedom for the set of effect sizes. If effectsize.df>0, the confidence intervals, pvalues and significance test use the t-distribution probability values. If effectsize.df=0 (default), the confidence intervals, the pvalues and significance test use the normal distribution probability values.
• alpha: The significance level (default 0.05) used to control the significance tests and calculation of confidence limits.

Returns

ES.test The value of the t-statistic

ES.pvalue The p-value of the two-sided t-test if the parameter d.df>0, or the normal probability value if d.df=0

ES.sig The significance of the statistical test of the d.tvalue return value at the alpha level for one sided tests and aplha/2 for two sided tests as specified by the input parameter alternative.

ES.ci.lower The lower 100*(1-alpha/2)

ES.ci.upper The upper 100*(1-alpha/2)

Examples

PHatES=mean(c(0.92,0.6,0.48,0.72,0.88))-0.5
PHatESvar=sum(c(0.01,0.04,0.05,0.04,0.01))/25
PHatdf=sum(c(6.63,6.63,5.08,5.61,8))
#PHattwosidedTestStatistics(effectsize=PHatES,effectsize.variance=PHatESvar)
# A tibble: 1 x 5
# ES.test ES.pvalue ES.sig ES.ci.lower ES.ci.upper
#     <dbl>     <dbl> <lgl>        <dbl>       <dbl>
# 1    2.84   0.00451 TRUE        0.0682       0.372
(effectsize=PHatES,effectsize.variance=PHatESvar,effectsize.df=PHatdf)
#  A tibble: 1 x 5
#   ES.test ES.pvalue ES.sig ES.ci.lower ES.ci.upper
#     <dbl>     <dbl> <lgl>        <dbl>       <dbl>
# 1    2.84   0.00778 TRUE        0.0622       0.378

Author(s)

Barbara Kitchenham and Lech Madeyski