Assessing normality and applying data transformationsIn lecture recently, we learned about the normal distribution and its applications.
Question:
Assessing normality and applying data transformationsIn lecture recently, we learned about the normal distribution and its applications. You will find thatmany analytical techniques require the assumption that data are sampled from a population with anormal distribution.
Today, you will examine two data sets to determine whether the data fit that assumption (i.e., whetherthey are approximately normally distributed). The data sets are:
A. The body mass index of a sample of men, in the mens’ health data set (posted on Blackboard).
B. Number of eastern mudminnows (Umbra pygmaea) in Maryland streams (posted on Blackboard).
1. For each of these data sets, use a series of methods to determine whether the data are normallydistributed:
(a) examination of a histogram;
(b) identification of outliers, if any;
(c) examination of a normal quantile plot (Q-Q plot);
(d) use of the Komolgorov-Smirnov test of normality. You can find this option under Analysis
Nonparametric Tests Legacy Dialogs. (Treat this like any other hypothesis test. The nullhypothesis is that the data are distributed normally. Be sure to provide the SPSS output onwhich you base your conclusions.)
If a data set is not normally distributed, some statistical analyses will produce biased results.Therefore, we need a way to convert the data to fit the assumption of normality. Attempts to do thisare called data transformations.
2. If either of the above data sets does not conform to the assumption of normality, try transformingthe data using each of the following techniques:
(a) taking the square root of each x;
(b) taking the log (x + 1) for each x;
(c) taking the reciprocal of each x;
(d) squaring each x.
(If both of the data sets are non-normal, do the data transformations for only one of them.)To transform your data, go to the Transformations menu and choose Compute Variable. This willallow you to specify what transformation you want to apply (by defining it mathematically) and savethe result of the transformation as a new variable.
There are other data transformations available besides the 4 examples we will use. Some are verycomplex (e.g., the Box-Cox transformation essentially fits all possible combinations of othertransformations until one works). These four should be enough to get you familiar with the procedure,however.
After conducting each transformation, report whether (and how well) the transformation hasimproved how well the data conform to the assumption of normality. Would any of thesetransformations make you comfortable conducting a hypothesis test that assumes normality? Why orwhy not?
Financial Management Principles and Applications
ISBN: 978-0134417219
13th edition
Authors: Sheridan Titman, Arthur J. Keown, John H. Martin