# Standardized mean difference

### Description

Function to calculate the standardized mean difference (regular or unbiased) using either raw data or summary measures.

### Usage

1 2 3 |

### Arguments

`Group.1` |
Raw data for group 1. |

`Group.2` |
Raw data for group 2. |

`Mean.1` |
The mean of group 1. |

`Mean.2` |
The mean of group 2. |

`s.1` |
The standard deviation of group 1 (i.e., the square root of the unbiased estimator of the population variance). |

`s.2` |
The standard deviation of group 2 (i.e., the square root of the unbiased estimator of the population variance). |

`s` |
The pooled group standard deviation (i.e., the square root of the unbiased estimator of the population variance). |

`n.1` |
The sample size within group 1. |

`n.2` |
The sample size within group 2. |

`Unbiased` |
Returns the unbiased estimate of the standardized mean difference. |

### Details

When `Unbiased=TRUE`

, the unbiased estimate of the standardized mean difference is returned (Hedges, 1981).

### Value

Returns the estimated standardized mean difference.

### Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

### References

Cohen, J. (1988). *Statistical power analysis for the behavioral sciences* (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.

Cumming, G. & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are
based on central and noncentral distributions, *Educational and Psychological Measurement, 61*, 532–574.

Hedges, L. V. (1981). Distribution theory for Glass's Estimator of effect size and related estimators. *Journal of Educational Statistics, 2*, 107–128.

Kelley, K. (2005) The effects of nonnormal distributions on confidence intervals around the standardized mean
difference: Bootstrap and parametric confidence intervals, *Educational and Psychological Measurement, 65*, 51–69.

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. *Journal of Statistical Software, 20* (8), 1–24.

Steiger, J. H., & Fouladi, R. T. (1997). Noncentrality interval estimation and the evaluation of
statistical methods. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.), *What if there were
no significance tests?* (pp. 221–257). Mahwah, NJ: Lawrence Erlbaum.

### See Also

`smd.c`

, `conf.limits.nct`

, `ss.aipe`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
# Generate sample data.
set.seed(113)
g.1 <- rnorm(n=25, mean=.5, sd=1)
g.2 <- rnorm(n=25, mean=0, sd=1)
smd(Group.1=g.1, Group.2=g.2)
M.x <- .66745
M.y <- .24878
sd <- 1.048
smd(Mean.1=M.x, Mean.2=M.y, s=sd)
M.x <- .66745
M.y <- .24878
n1 <- 25
n2 <- 25
sd.1 <- .95817
sd.2 <- 1.1311
smd(Mean.1=M.x, Mean.2=M.y, s.1=sd.1, s.2=sd.2, n.1=n1, n.2=n2)
smd(Mean.1=M.x, Mean.2=M.y, s.1=sd.1, s.2=sd.2, n.1=n1, n.2=n2,
Unbiased=TRUE)
``` |

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