Crawford and Howell's (1998) modified t-test. Takes a single observation and compares it to a distribution estimated by a control sample. Calculates standardised difference between the case score and the mean of the controls and proportions falling above or below the case score, as well as associated confidence intervals.
TD(
case,
controls,
sd = NULL,
sample_size = NULL,
alternative = c("less", "greater", "two.sided"),
conf_int = TRUE,
conf_level = 0.95,
conf_int_spec = 0.01,
na.rm = FALSE
)A list of class "htest" containing the following components:
statistic | the value of the t-statistic. | parameter | |
| the degrees of freedom for the t-statistic. | p.value | the p-value for the test. | |
estimate | estimated standardised difference (Z-CC) and point estimate of p-value. | ||
null.value | the value of the difference under the null hypothesis. | interval | |
| named numerical vector containing level of confidence and confidence intervals for both Z-CC and p-value. | desc | named numerical containing descriptive statistics: mean and standard deviations of controls as well as sample size and standard error used in the t-formula. | |
alternative | a character string describing the alternative hypothesis. | ||
method | a character string indicating what type of t-test was performed. | data.name |
Case observation, can only be a single value.
Numeric vector of observations from the control sample. If single value, treated as mean.
If input of controls is single value, the standard deviation of the sample must be given as well.
If input of controls is single value, the size of the sample must be gven as well.
A character string specifying the alternative hypothesis,
must be one of "less" (default), "greater" or
"two.sided". You can specify just the initial letter.
Initiates a search algorithm for finding confidence
intervals. Defaults to TRUE, set to FALSE for faster
calculation (e.g. for simulations).
Level of confidence for intervals, defaults to 95%.
The size of iterative steps for calculating confidence intervals. Smaller values gives more precise intervals but takes longer to calculate. Defaults to a specificity of 0.01.
Remove NAs from controls.
Calculating the confidence intervals relies on finding non-centrality
parameters for non-central t-distributions. Depending on the degrees of
freedom, the confidence level and the effect size exact accuracy from the
stats::qt() function used can not be guaranteed. However, the
approximations should be good enough for most cases.
See https://stat.ethz.ch/pipermail/r-help/2008-June/164843.html.
Returns the point estimate of the standardised difference between the case score and the mean of the controls and the point estimate of the p-value (i.e. the percentage of the population that would be expected to obtain a lower or higher score, depending on the alternative hypothesis).
Crawford, J. R., & Howell, D. C. (1998). Comparing an Individual's Test Score Against Norms Derived from Small Samples. The Clinical Neuropsychologist, 12(4), 482 - 486. tools:::Rd_expr_doi("10.1076/clin.12.4.482.7241")
Crawford, J. R., & Garthwaite, P. H. (2002). Investigation of the single case in neuropsychology: Confidence limits on the abnormality of test scores and test score differences. Neuropsychologia, 40(8), 1196-1208. tools:::Rd_expr_doi("10.1016/S0028-3932(01)00224-X")
TD(case = -2, controls = 0, sd = 1, sample_size = 20)
TD(case = size_weight_illusion[1, "V_SWI"],
controls = size_weight_illusion[-1, "V_SWI"], alternative = "l")
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