omega.partial.SS.rm: Partial Omega Squared for Repeated Measures ANOVA from F
In MOTE: Effect Size and Confidence Interval Calculator

Description Usage Arguments Details Value Examples

This function displays omega squared from ANOVA analyses and its non-central confidence interval based on the F distribution. This formula is appropriate for multi-way repeated measures designs and mix level designs.

1	omega.partial.SS.rm(dfm, dfe, msm, mse, mss, ssm, sse, sss, a = 0.05)

`dfm`	degrees of freedom for the model/IV/between
`dfe`	degrees of freedom for the error/residual/within
`msm`	mean square for the model/IV/between
`mse`	mean square for the error/residual/within
`mss`	mean square for the subject variance
`ssm`	sum of squares for the model/IV/between
`sse`	sum of squares for the error/residual/within
`sss`	sum of squares for the subject variance
`a`	significance level

Partial omega squared is calculated by subtracting the mean square for the error from the mean square of the model, which is multiplied by degrees of freedom of the model. This is divided by the sum of the sum of squares for the model, sum of squares for the error, sum of squares for the subject, and the mean square of the subject.

omega_p^2 = (dfm x (msm - mse)) / (ssm + sse + sss + mss)

The F-statistic is calculated by dividing the mean square of the model by the mean square of the error.

F = msm / mse

Learn more on our example page.

Provides omega squared with associated confidence intervals and relevant statistics.

`omega`	omega squared
`omegalow`	lower level confidence interval of omega
`omegahigh`	upper level confidence interval of omega
`dfm`	degrees of freedom for the model/IV/between
`dfe`	degrees of freedom for the error/resisual/within
`F`	F-statistic
`p`	p-value
`estimate`	the omega squared statistic and confidence interval in APA style for markdown printing
`statistic`	the F-statistic in APA style for markdown printing

#The following example is derived from the "rm2_data" dataset, included
#in the MOTE library.

#In this experiment people were given word pairs to rate based on
#their "relatedness". How many people out of a 100 would put LOST-FOUND
#together? Participants were given pairs of words and asked to rate them
#on how often they thought 100 people would give the second word if shown
#the first word.  The strength of the word pairs was manipulated through
#the actual rating (forward strength: FSG) and the strength of the reverse
#rating (backward strength: BSG). Is there an interaction between FSG and
#BSG when participants are estimating the relation between word pairs?

library(ez)
library(reshape)
long_mix = melt(rm2_data, id = c("subject", "group"))
long_mix$FSG = c(rep("Low-FSG", nrow(rm2_data)),
                 rep("High-FSG", nrow(rm2_data)),
                 rep("Low-FSG", nrow(rm2_data)),
                 rep("High-FSG", nrow(rm2_data)))
long_mix$BSG = c(rep("Low-BSG", nrow(rm2_data)*2),
                 rep("High-BSG", nrow(rm2_data)*2))

anova_model = ezANOVA(data = long_mix,
                      dv = value,
                      wid = subject,
                      within = .(FSG, BSG),
                      detailed = TRUE,
                      type = 3)

#You would calculate one partial GOS value for each F-statistic.
#You can leave out the MS options if you include all the SS options.
#Here's an example for the interaction with typing in numbers.
omega.partial.SS.rm(dfm = 1, dfe = 157,
                    msm = 2442.948 / 1,
                    mse = 5402.567 / 157,
                    mss = 76988.130 / 157,
                    ssm = 2442.948, sss = 76988.13,
                    sse = 5402.567, a = .05)

#Here's an example for the interaction with code.
omega.partial.SS.rm(dfm = anova_model$ANOVA$DFn[4],
                  dfe = anova_model$ANOVA$DFd[4],
                  msm = anova_model$ANOVA$SSn[4] / anova_model$ANOVA$DFn[4],
                  mse = anova_model$ANOVA$SSd[4] / anova_model$ANOVA$DFd[4],
                  mss = anova_model$ANOVA$SSd[1] / anova_model$ANOVA$DFd[1],
                  ssm = anova_model$ANOVA$SSn[4],
                  sse = anova_model$ANOVA$SSd[4],
                  sss = anova_model$ANOVA$SSd[1],
                  a = .05)