Ebook Handbook of biolological statistics (3/E): Part 2
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Ebook Handbook of biolological statistics (3/E): Part 2
Ebook Handbook of biolological statistics (3/E): Part 2
Handbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2ere I explain how to check this and what to do if the data aren't normal.IntroductionDry veight of amphipod harhlings, microgramsHistogram of dry weights of the amphipod crustacean Plfitorchestia plateiisis.A probability distribution specifies the probability of getting an observation in a particula Ebook Handbook of biolological statistics (3/E): Part 2r range of values; the normal distribution is the familiar bell-shaped curve, with a nigh probability of getting an observation near the middle and loEbook Handbook of biolological statistics (3/E): Part 2
wer probabilities as you get further from the middle. A normal distribution can be completely described by just two numbers, or parameters, the mean aHandbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2ons of an anova and other tests for measurement variables is that the data fit the normal probability distribution. Because these tests assume that the data can be described by two parameters, the mean and standard deviation, they are called parametric tests.When you plot a frequency histogram of me Ebook Handbook of biolological statistics (3/E): Part 2asurement data, the frequencies should approximate the bell-shaped normal distribution. For example, the figure shown at the right is a histogram of dEbook Handbook of biolological statistics (3/E): Part 2
ry weights of newly hatched amphipods ịPỉatorches da platensis), data 1 tediously collected’for my Ph.D. research. It fits the normal distribution preHandbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2e a large number of random numbers, the means of those numbers are approximately normally distributed. If you think of a variable like weight as resulting from the effects of a bunch of other variables averaged together—age, nutrition, disease exposure, the genotype of several genes, etc—it's not su Ebook Handbook of biolological statistics (3/E): Part 2rprising that it would be normally distributed.134NormalityEgg masses per remale treehopperTwo non-normal histograms.Other data sets don't fit the norEbook Handbook of biolological statistics (3/E): Part 2
mal distribution very’ well. The histogram on the left is the level of sulphate in Maryland streams (data from the Maryland Biological Stream Survey, Handbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2 sulphate. The histogram on the right is the number of egg masses laid by indivuduals of the lentago host race of the treehopper Endienopa (unpublished data courtesy of Michael Cast). The curve is bimodal, with one peak at around 14 egg masses and the other at zero.Parametric tests assume that your Ebook Handbook of biolological statistics (3/E): Part 2data fit the normal distribution. If your measurement variable is not normally distributed, you may be increasing your chance of a false positive resuEbook Handbook of biolological statistics (3/E): Part 2
lt if you analyze the data with a test that assumes normality.What to do about non-normalityOnce you have collected a set of measurement data, you shoHandbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2ribution, but I don’t recommend them, because many data sets that are significantly non-normal would be perfectly appropriate for an anova or other parametric test. Fortunately, an anova is not very sensitive to moderate deviations from normality’; simulation studies, using a variety of’non-normal d Ebook Handbook of biolological statistics (3/E): Part 2istributions, have shown that the false positive rate is not affected very much by this violation of the assumption (Glass et al. 1972, Harwell et al.Ebook Handbook of biolological statistics (3/E): Part 2
1992, Lix et al. 1996). This is another result of the central limit theorem, which says that when you take a large number of random samples from a poHandbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2ry sensitive to deviations from normality’, I recommend that you don't worry about it unless your data appear very, very’ non-normal to you. This IS a subjective judgement on your part, but there don't seem to be any’ objective rules on how much lion-normality IS too much for a parametric test. You Ebook Handbook of biolological statistics (3/E): Part 2should look at what other people in your field do; if everyone transforms the kind of data you're collecting, pr uses a non-parametric test, you shoulEbook Handbook of biolological statistics (3/E): Part 2
d consider doing what everyone else does even if the non-normality doesn't seem that bad to you.If your histogram looks like a normal distribution thaHandbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2ok more normal. It's best if you collect some data, check the normality’, and decide on a transformation before you rún your actual experiment; you don't want cynical people to think that you tried different transformations until you found one that gave you a signficant result for your experiment.13 Ebook Handbook of biolological statistics (3/E): Part 25Handbook of Biological StatisticsIf your data still look severely non-normal no matter what transformation you apply, it's probably still okay to anaEbook Handbook of biolological statistics (3/E): Part 2
lyze the data using a parametric lest; they're just not that sensitive to non-normalily. However, you may want to analyze your data using a nonparametHandbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2lcoxon signed-rank tost instead of a paired f-lesl, and Spearman rank correlation instead of linear regression/correlation. I hose non-parametric tests do not assume that the data fit the normal distribution. I hey do assume that the data in different groups have the same distribution as each other, Ebook Handbook of biolological statistics (3/E): Part 2 however; if different groups have ditferenl shaped distributions (for example, one is skewed to the left, another is skewed to the right), a non-paraEbook Handbook of biolological statistics (3/E): Part 2
metric lest will not be any better than a parametric one.Skewness and kurtosisnormalpiatykurtlcleptokurtlcGraphs illustrating skewness and kurtosis.A Handbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2left side is said to be skewed to the left. There is a statistic to describe skewness, g, but I don't know of any reason to calculate it; there is no rule of thumb that you shouldn't do a parametric test if is greater than some cutoff value.Another way in which data can deviate from the normal distr Ebook Handbook of biolological statistics (3/E): Part 2ibution is kurtosis. A histogram that has a high peak in the middle and long tails on either side is leplokurlic; a histogram with a broad, flat middlEbook Handbook of biolological statistics (3/E): Part 2
e and short tails is platykurtic. I ho statistic to describe kurlosis isỵa but I can't think of any reason why you'd want to calculate it, either.How Handbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). He Ebook Handbook of biolological statistics (3/E): Part 2sformed data (www.biostathandbook.com/lTistogram.xls). Il will handle up to 1000 observations.136NormalityIf there are not enough observations in each group to check normality, you may want to examine the residuals (each observation minus the mean of its group): To do this, open a separate spreadshe Ebook Handbook of biolological statistics (3/E): Part 2et and put the numbers from each group in a separate column. Then create columns with the mean of each group subtracted from each observation in its gEbook Handbook of biolological statistics (3/E): Part 2
roup, as shown below. Copy these numbers into the histogram spreadsheet.e I -B2-BS13Handbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). HeHandbook of Biological statisticsNormalityMost tests tor measurement variables assume that data are normally distributed (fit a bell-shaped curve). HeGọi ngay
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