Try to choose a power that reflects an underlying physical reality.
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The choice of power exponent is not trivial. Usually, data is raised to the second power (squared). It can affect the characteristics of the transformed variable.Ģ) Data may have a physical (power) component, such as area vs. Dependingon the range of values, this transformation is the most powerful in reducing negative skew. This transformation can be performed on negative numbers. This transformation cannot be performed on non-positive values.Ģ) You suspect an underlying logarithmic trend (decay, attrition, survival. The variable should not have values close to zero. This transformation cannot be performed on negative data.Ģ) Data may have been originally derived by division, or represents The base of the logarithm is essentially arbitrary (results will only differ by a linear, multiplicative factor), though the most commonģ) Data have many zero's or extremely small values.Ĥ) Data may have a physical (power) component, such as area vs. This transformation cannot be performed on non-positive data. Is added to the variable before the transformation is applied.Ģ) You suspect an exponential component in the data.ģ) Data might be best classified by orders-of-magnitude.Ĥ) Cumulative main effects are multiplicative, rather than additive. Many transformations cannot be applied to negative or zero values. The secondary attribute to consider is whether the variable contains negative values or zero. If group means are negatively correlated with group variances, the data may be negatively skewed. If group means are positively correlated with group variances (or standard deviations), the data may be positively skewed. Skewness may also be discerned from the variable's characteristics across groups. Where values cannot rise higher (nearly everybody scores near 100% correct on a test). Negatively skewed data may be subject to a "ceiling," Positively skewed data may be subject to a "floor," where values cannot drop lower (nearly everybody scores near 0% correct on a test). The primary attribute for deciding upon a transformation is whether the data is positively skewed (skewed to right, skew > 0) or negatively skewed (skewed to left, skew < 0). You will then want to re-test the normality assumption before considering transformations. If you find outliers that were created by incorrect data entry, correct them. Extreme outliers may be the result of incorrect data entry (or computation). Double-check that these outliers have been coded correctly. These transformations are what you should first use.Ĭheck the data for extreme outliers.
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Before using any of these transformations, determine which transformations, if any, are commonly used in your field of research. Some transformation options are offered below.