The red line is a model CDF, the blue line is an empirical CDF, and the black arrow is the K–S statistic. Substitute for log10(x) in equation 2 and cancel out ln(x)ĭr Kathy Taylor teaches data extraction in Meta-analysis. This is a short course that is also available as part of our MSc in Evidence-Based Health Care, MSc in EBHC Medical Statistics, and MSc in EBHC Systematic Reviews.Illustration of the Kolmogorov–Smirnov statistic. Taking logs of base 10 of both sides and using 3rd law of logs
In calculators, it is given as e x , and this may have its own button, as on a mobile phone app, or it may be accessed on a hand-held calculator by pressing the SHIFT and ln keys in sequence. This is written as exp(x) in R, SAS and STATA, and EXP(x) in SPSS and EXCEL.
To antilog (cancel out) natural logs, we use the exponential function. On calculators, the button to calculate the natural log of a number is ln. In computer programs and software packages, natural logs of x is written as log(x) in R and SAS, LN(x) in SPSS and EXCEL, and either ln(x) or log(x) in STATA. A bit of maths (see below if you’re interested) shows us In some sciences, logs to base 10, also known as the ‘common logarithm’ is more common. Medical statisticians typically use natural logs. I will write the natural log of x as In(x). In my blog, when I refer to logs I will mean ‘natural’ logs for which the base is e, known as Euler’s number, and it is equal to 2.718 to 3 decimal places. When plotting graphs, log-transforming makes curved data fall on lines which are more straight, and ‘flattens’ data, drawing in extreme values which enables patterns in the data to be seen more clearly.
Medical statisticians log-transform skewed data to make the distribution of the data more symmetrical and this helps data ‘behave better’ by meeting the assumptions of statistical models.
Logarithms (frequently referred to as ‘logs’) are often used in statistics.
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