Test a hypothesis about a difference in correlation strength

test_rdiff is suitable for testing a hypothesis about a difference in correlation (r) between two conditions. At the moment, it can only test hypotheses for independent-group designs.

Usage

test_rdiff(estimate, rope = c(0, 0), output_html = FALSE)

Arguments

estimate

An esci_estimate object generated by an estimate_rdiff_ function

rope

A two-element vector defining the Region of Practical Equivalence (ROPE). Specify c(0, 0) to test a point null of exactly 0. Specify any two ascending values between -1 and 1 to test an interval null (e.g. c(-.25, .25) to test the hypothesis that the difference in correlation is between -.25 and .25).

output_html

TRUE to return results in HTML; FALSE (default) to return standard output

Value

Returns a list with 1-2 data frames

point_null - always returned
- test_type - 'Nil hypothesis test', meaning a test against H0 = 0
- outcome_variable_name - Name of the outcome variable
- effect - Label for the effect being tested
- null_words - Express the null in words
- confidence - Confidence level, integer (95 for 95%, etc.)
- LL - Lower boundary of the confidence% CI for the effect
- UL - Upper boundary of the confidence% CI for the effect
- CI - Character representation of the CI for the effect
- CI_compare - Text description of relation between CI and null
- t - If applicable, t value for hypothesis test
- df - If applicable, degrees of freedom for hypothesis test
- p - If applicable, p value for hypothesis test
- p_result - Text representation of p value obtained
- null_decision - Text represention of the decision for the null
- conclusion - Text representation of conclusion to draw
- significant - TRUE/FALSE if significant at alpha = 1-CI
interval_null - returned only if an interval null is specified
- test_type - 'Practical significance test', meaning a test against an interval null
- outcome_variable_name -
- effect - Name of the outcome variable
- rope - Test representation of null interval
- confidence - Confidence level, integer (95 for 95%, etc.)
- CI - Character representation of the CI for the effect
- rope_compare - Text description of relation between CI and null interval
- p_result - Text representation of p value obtained
- conclusion - Text representation of conclusion to draw
- significant - TRUE/FALSE if significant at alpha = 1-CI

Details

This function can be passed an esci_estimate object generated by estimate_rdiff_two().

It can test hypotheses about a specific value for the difference (a point null) or about a range of values (an interval null)

Examples

# example code
estimate <- esci::estimate_rdiff_two(
  comparison_r = .53,
  comparison_n = 45,
  reference_r = .41,
  reference_n = 59,
  grouping_variable_levels = c("Females", "Males"),
  x_variable_name = "Satisfaction with life",
  y_variable_name = "Body satisfaction",
  grouping_variable_name = "Gender",
  conf_level = .95
)
test_rdiff(estimate)
#> $properties
#> $properties$effect_size_name
#> [1] "r"
#> 
#> $properties$alpha
#> [1] 0.05
#> 
#> $properties$interval_null
#> [1] FALSE
#> 
#> $properties$rope
#> [1] 0 0
#> 
#> $properties$rope_units
#> [1] "raw"
#> 
#> 
#> $point_null
#>             test_type                        outcome_variable_name
#> 1 Nil Hypothesis Test Satisfaction with life and Body satisfaction
#>              effect null_words confidence         LL        UL
#> 1 Males  -  Females       0.00         95 -0.1987466 0.4209803
#>                               CI              CI_compare         t df         p
#> 1 95% CI [-0.1987466, 0.4209803] The 95% CI contains H_0 0.7570586 NA 0.4490148
#>   p_result      null_decision
#> 1 p ≥ 0.05 Fail to reject H_0
#>                                              conclusion significant
#> 1 At α = 0.05, 0.00 remains a plausible value of Ͱ_diff       FALSE
#>