effect_size_additive {multiplestressR}

Additive Null Model

Description

Calculate the additive null model for one, or more, experiments.

Usage

effect_size_additive(
  Control_N,
  Control_SD,
  Control_Mean,
  StressorA_N,
  StressorA_SD,
  StressorA_Mean,
  StressorB_N,
  StressorB_SD,
  StressorB_Mean,
  StressorsAB_N,
  StressorsAB_SD,
  StressorsAB_Mean,
  Small_Sample_Correction,
  Significance_Level
)

Arguments

Control_N

Sample size of the control treatment (numeric)

Control_SD

Standard deviation of the control treatment (numeric)

Control_Mean

Mean value of the control treatment (numeric)

StressorA_N

Sample size of stressor A treatment (numeric)

StressorA_SD

Standard deviation of stressor A treatment (numeric)

StressorA_Mean

Mean value of stressor A treatment (numeric)

StressorB_N

Sample size of stressor B treatment (numeric)

StressorB_SD

Standard deviation of stressor B treatment (numeric)

StressorB_Mean

Mean value of stressor B treatment (numeric)

StressorsAB_N

Sample size of stressors A and B treatment (numeric)

StressorsAB_SD

Standard deviation of stressors A and B treatment (numeric)

StressorsAB_Mean

Mean value of stressors A and B treatment (numeric)

Small_Sample_Correction

Whether the correction for small sample sizes should be enacted (TRUE or FALSE; default is TRUE)

Significance_Level

The value of alpha for which confidence intervals are calculated (numeric, between 0 and 1; default is 0.05)

Details

The form of the additive null model used here is taken from Gurevitch et al. (2000).

Interaction effect sizes, variances, and confidence intervals are calculated.

Here, the factorial form of Hedges' d is calculated.

Value

The function returns a dataframe containing

i. effect sizes

ii. effect size variances

iii. upper and lower confidence intervals

iv. user specified numeric parameters

The equations used to calculate effect sizes, effect size variances, and confidence intervals are described in Burgess et al. (2021).

Note that the parameter Small_Sample_Correction determines whether the correction for sample sizes is to be used within the function. This correction (see Borenstein et al. (2009)) tends towards 1 as sample sizes increase. Hence it is most applicable where small sample sizes are used.

References

Borenstein, M., Cooper, H., Hedges, L., & Valentine, J. (2009). Effect sizes for continuous data. The Handbook of Research Synthesis and Meta-Analysis, 2, 221-235.

Burgess, B. J., Jackson, M. C., & Murrell, D. J. (2021). Multiple stressor null models frequently fail to detect most interactions due to low statistical power. bioRxiv.

Gurevitch, J., Morrison, J. A., & Hedges, L. V. (2000). The interaction between competition and predation: a meta-analysis of field experiments. The American Naturalist, 155(4), 435-453.

Examples

df <- effect_size_additive(Control_N = 4,
                    Control_SD = 0.114,
                    Control_Mean = 0.90,
                    StressorA_N = 4,
                    StressorA_SD = 0.11,
                    StressorA_Mean = 0.77,
                    StressorB_N = 3,
                    StressorB_SD = 0.143,
                    StressorB_Mean = 0.72,
                    StressorsAB_N = 4,
                    StressorsAB_SD = 0.088,
                    StressorsAB_Mean = 0.55,
                    Small_Sample_Correction = TRUE,
                    Significance_Level = 0.05)

#loading up an example dataset from the multiplestressR package
df <- multiplestressR::survival

#calculating effect sizes
df <- effect_size_additive(Control_N         = df$Sample_Size_Control,
                           Control_SD        = df$Standard_Deviation_Control,
                           Control_Mean      = df$Mean_Control,
                           StressorA_N       = df$Sample_Size_Temperature,
                           StressorA_SD      = df$Standard_Deviation_Temperature,
                           StressorA_Mean    = df$Mean_Temperature,
                           StressorB_N       = df$Sample_Size_pH,
                           StressorB_SD      = df$Standard_Deviation_pH,
                           StressorB_Mean    = df$Mean_pH,
                           StressorsAB_N     = df$Sample_Size_Temperature_pH,
                           StressorsAB_SD    = df$Standard_Deviation_Temperature_pH,
                           StressorsAB_Mean  = df$Mean_Temperature_pH,
                           Significance_Level = 0.05);