Log transformation 

If the option Log transformation was selected, the program will display the back transformed results.  The 

back transformed mean is named the Geometric mean.  Variance, Standard deviation and Standard error 

of the mean cannot be back transformed meaningfully and are not reported. 

Presentation of results 

The description of the data in a publication will include the sample size and arithmetic mean.  The standard 

deviation can be given as an indicator of the variability of the data: the mean was 25.6 mm (SD 3.2 mm).  

The standard error of the mean can be given to show the precision of the mean: the mean was 25.6 mm 

(SE 1.6 mm).   

When you want to make an inference about the population mean, you can give the mean and the 95% 

confidence interval of the mean: the mean was 25.6 (95% CI 22.4 to 28.8). 

If the distribution of the variable is positively skewed, then a mathematical transformation of the data may 

be applied to obtain a Normal distribution, e.g. a logarithmic or square root transformation.  After 

calculations you can convert the results back to the original scale.  It is then useless to report the back 

transformed standard deviation or standard error of the mean.  Instead, you can antilog the confidence 

interval in case a logarithmic transformation was applied, or square the confidence interval if you have 

applied a square root transformation (Altman et al., 1983).  The resulting confidence interval will then not 

be symmetrical, reflecting the shape of the distribution.  If, for example, after logarithmic transformation of 

the data, the mean is 1.408 and the 95% confidence interval is 1.334 to 1.482, then you will antilog these 

statistics and report: the mean was 25.6 mm (95% CI 21.6 to 30.3). 

If the distribution of the variable is not normal even after logarithmic or other transformation, then it is better 

to report the median and a percentiles range, e.g. the interquartile range, or the 90% or 95% central range: 

the median was 25.6 mm (95% central range 19.6 to 33.5 mm).  The sample size will be taken into 

consideration when you decide whether to use the interquartile range or the 90% or 95% central range 

(see p. 46) (Altman, 1980). 

The precision of the reported statistics should correspond to the precision of the original data.  The mean 

and 95% CI can be given to one decimal place more than the raw data, the standard deviation and 

standard error can be given with one extra decimal (Altman et al., 1983). 

Finally, the summary statistics in the text or table may be complemented by a graph (see p. 52). 

Histogram 

After selecting Histogram, a similar dialog box is displayed as for Summary statistics. Enter the name of a 

variable and optionally a selection criterion.  If you have previously entered this variable and selection 

criterion in the box for summary statistics, then this new variable will be selectable in the Variable list (click 

the 

 button). 

After a moment (the program first collects the data and performs some calculations) the following dialog 

box is displayed on the screen: 

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