Repeated Summary Correlations

This page analyzes a set of correlations among variables using summary statistics input.

Preliminary Tasks

Data Entry

This code inputs the variable summaries and creates a summary table.

Outcome1 <- c(N = 10, M = 8.000, SD = 1.414)
Outcome2 <- c(N = 10, M = 11.000, SD = 2.211)
Outcome3 <- c(N = 10, M = 12.000, SD = 2.449)
RepeatedMoments <- construct(Outcome1, Outcome2, Outcome3, class = "wsm")

This code creates a correlation matrix.

Outcome1 <- c(1.000, .533, .385)
Outcome2 <- c(.533, 1.000, .574)
Outcome3 <- c(.385, .574, 1.000)
RepeatedCorrs <- construct(Outcome1, Outcome2, Outcome3, class = "cor")

Summary Statistics

This code confirms the descriptive statistics from the summary tables.

(RepeatedMoments) |> describeMoments()

Summary Statistics for the Data

               N       M      SD
Outcome1  10.000   8.000   1.414
Outcome2  10.000  11.000   2.211
Outcome3  10.000  12.000   2.449

(RepeatedCorrs) |> describeCorrelations()

Correlations for the Data

         Outcome1 Outcome2 Outcome3
Outcome1   1.000    0.533    0.385 
Outcome2   0.533    1.000    0.574 
Outcome3   0.385    0.574    1.000 

Analyses of a Correlation

This section produces analyses of a single correlation.

Scatterlot and Confidence Ellipse

This code provides a confidence ellipse for the bivariate relationship. Because there is no raw data, no data points are visible and the code defaults instead to an ellipse.

(RepeatedMoments) |> focus(Outcome1, Outcome2) |> plotScatter(RepeatedCorrs)

The ellipse can be altered for different confidence levels.

(RepeatedMoments) |> focus(Outcome1, Outcome2) |> plotScatter(RepeatedCorrs, conf.level = .99)

Confidence Interval

This code will provide the confidence interval for the correlation.

(RepeatedMoments) |> focus(Outcome1, Outcome2) |> estimateCorrelations(RepeatedCorrs)

Confidence Intervals for the Correlations

                          R      SE      LL      UL
Outcome1 & Outcome2   0.533   0.378  -0.145   0.870

This code will produce a graph of the confidence interval for the correlation.

(RepeatedMoments) |> focus(Outcome1, Outcome2) |> plotCorrelations(RepeatedCorrs)

The code defaults to 95% confidence intervals. This can be changed if desired.

(RepeatedMoments) |> focus(Outcome1, Outcome2) |> estimateCorrelations(RepeatedCorrs, conf.level = .99)

Confidence Intervals for the Correlations

                          R      SE      LL      UL
Outcome1 & Outcome2   0.533   0.378  -0.362   0.917

Of course, it is possible to change from the default confidence level in the graph. It is also possible to add a comparison value and a region of practical equivalence.

(RepeatedMoments) |> focus(Outcome1, Outcome2) |> plotCorrelations(RepeatedCorrs, conf.level = .99, line = 0, rope = c(-.2, .2))

Significance Test

This code will produce a table of NHST for the correlation (against a value of zero).

(RepeatedMoments) |> focus(Outcome1, Outcome2) |> testCorrelations(RepeatedCorrs)

Hypothesis Tests for the Correlations

                          R      SE      df       t       p
Outcome1 & Outcome2   0.533   0.299   8.000   1.782   0.113

Analyses of Several Correlations

This section analyzes the correlations among multiple variables.

Confidence Intervals

This code will provide the confidence intervals for the correlations.

(RepeatedMoments) |> estimateCorrelations(RepeatedCorrs)

Confidence Intervals for the Correlations

                          R      SE      LL      UL
Outcome1 & Outcome2   0.533   0.378  -0.145   0.870
Outcome1 & Outcome3   0.385   0.378  -0.323   0.817
Outcome2 & Outcome3   0.574   0.378  -0.087   0.884

This code will produce a graph of the confidence intervals for the correlations.

(RepeatedMoments) |> plotCorrelations(RepeatedCorrs)

The code defaults to 95% confidence intervals. This can be changed if desired.

(RepeatedMoments) |> estimateCorrelations(RepeatedCorrs, conf.level = .99)

Confidence Intervals for the Correlations

                          R      SE      LL      UL
Outcome1 & Outcome2   0.533   0.378  -0.362   0.917
Outcome1 & Outcome3   0.385   0.378  -0.514   0.881
Outcome2 & Outcome3   0.574   0.378  -0.310   0.926

Of course, it is possible to change from the default confidence level in the graph. It is also possible to add a comparison value and a region of practical equivalence.

(RepeatedMoments) |> plotCorrelations(RepeatedCorrs, conf.level = .99, line = 0, rope = c(-.2, .2))

Significance Tests

This code will produce a table of NHST for the correlations (against a value of zero).

(RepeatedMoments) |> testCorrelations(RepeatedCorrs)

Hypothesis Tests for the Correlations

                          R      SE      df       t       p
Outcome1 & Outcome2   0.533   0.299   8.000   1.782   0.113
Outcome1 & Outcome3   0.385   0.326   8.000   1.180   0.272
Outcome2 & Outcome3   0.574   0.290   8.000   1.983   0.083