Data Transformation.ppt
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This document discusses data transformation techniques for statistical analysis. It explains that if measurement data is not normally distributed or has unequal variances, transformation is necessary. It then outlines steps to test for normality in SPSS. The document focuses on three common transformations: logarithmic for count data with a wide range, square root for rare count events, and arcsine for proportional or percentage data to make distributions normal. Examples and formulas are provided for each transformation.
Data Transformation.ppt
- 1. “Strengthening the Research Capacity through Statistical Interventions” Dr. Jitendra Kumar Chaudhary Assistant Professor Department of Animal Genetics & Breeding, CVSc. & A.H., Central Agricultural University (CAU), Selesih, Aizawl, Mizoram-796014 Email-vetjitu@gmail.com
- 2. Data Transformation: If a measurement variable does not fit a normal distribution or has greatly different standard deviations in different groups, you should go for data transformation. Normality Test: 1)Skewness & Kurtosis 2) Shapiro Wilk test 3) Histogram
- 3. Procedure to test normality in SPSS Go to analyze, descriptive explore, take measurement in dependent and group in factor box tick on plots, tick on histogram and normality plots with test, continue and ok. Results Divide the skewness and kurtosis by std. error and see if the values lies between -1.96 to +1.96 then the data are normally distributed (a minor difference is also normally distributed). See that the Shapiro wilk test is significant or not, if it is non- significant means data is normal otherwise data is not normal.
- 4. The following are the three transformations, which are being used most commonly, in biological research a) Logarithmic Transformation b) Square root Transformation c) Arc sine or Angular Transformation
- 5. Logarithmic transformation for whole number counts with wide range This transformation is suitable for the data where the variance is proportional to the square of the mean or the coefficient of the variation (S.D./Mean) is constant or where effects are multiplicative. These conditions are generally found in the data that are whole numbers and cover a wide range of values. For example- number of insect per plot, number of egg mass per plant or per unit area etc.
- 6. Natural logarithm of a positive number=LN (Give cell number for which transformation to be done), Natural logarithm is based on the constant e (2.718281828845904) Logarithm of a positive number at base 10=Log10 (Give cell number for which transformation to be done), Or Log (number, 10)
- 7. Square root transformation The transformation is appropriate for the data sets where the variance is proportional to the mean. Here the data consists of small whole numbers, for example data obtained in counting rare events, such as number of infested plants in a plot, the number of insects caught in traps, number of weeds per plot.
- 8. Square root transformation These data sets generally follow the Poisson distribution and square root transformation approximates Poisson to normal distribution. Square root transformation=SQRT (Give cell number for which transformation to be done)
- 9. Arcsine Transformation for Proportions or Percentage The transformation is appropriate for the data on proportion i.e. data obtained from a count and the data expressed as decimal fraction and percentage. The distribution of percentage is binomial and this transformation makes the distribution normal. Arcsine Transformation=ASIN (Cell Identification e.g. (0.05)*(180)*(7/22) result will be in degrees.