When should I use the Shapiro-Wilk test? Remember that some tests, such as chi squared, can be used under various circumstances. The goal of the test changes based on the situation. Pay attention to the specific conditions noted in parenthesis to ensure you are picking the correct goal. A. Test the fit of the normal distribution to the data set. B. Test to see if the frequency data from a population fit a discrete probability distribution. C. Compare two treatment groups consisting of independent samples with a normal distribution AND unequal variance. D. Test if the median of a data set equals a null hypothesized value when the distribution of the data does not meet the assumption of normalacy. E. Compare two treatments consisting of paired data where a normal distribution can be assumed. F. Compare categorical frequency data with an expected population proportion. No difference between observed and expected proportions is used as the null hypothesis. G. Compare two treatment groups consisting of paired data when the data do not fit the normal distribution. H. Compares numerical data to a known mean. The null hypothesis is that the mean of the data equals the known mean. I. More than two treatment groups where a normal distribution can be assumed. J. Compare two treatment groups when a normal distribution cannot be assumed. K. Compare more than two treatment groups when a normal distribution cannot be met. L. Test to compare frequency data to a specific population model M. Compare two treatment groups of independent samples where the data meet the assumption that the data fit the normal distribution.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
When should I use the Shapiro-Wilk test?
Remember that some tests, such as chi squared, can be used under various circumstances. The goal of the test changes based on the situation. Pay attention to the specific conditions noted in parenthesis to ensure you are picking the correct goal.
| A. |
Test the fit of the |
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| B. |
Test to see if the frequency data from a population fit a discrete probability distribution. |
|
| C. |
Compare two treatment groups consisting of independent samples with a normal distribution AND unequal variance. |
|
| D. |
Test if the |
|
| E. |
Compare two treatments consisting of paired data where a normal distribution can be assumed. |
|
| F. |
Compare categorical frequency data with an expected population proportion. No difference between observed and expected proportions is used as the null hypothesis. |
|
| G. |
Compare two treatment groups consisting of paired data when the data do not fit the normal distribution. |
|
| H. |
Compares numerical data to a known mean. The null hypothesis is that the mean of the data equals the known mean. |
|
| I. |
More than two treatment groups where a normal distribution can be assumed. |
|
| J. |
Compare two treatment groups when a normal distribution cannot be assumed. |
|
| K. |
Compare more than two treatment groups when a normal distribution cannot be met. |
|
| L. |
Test to compare frequency data to a specific population model |
|
| M. |
Compare two treatment groups of independent samples where the data meet the assumption that the data fit the normal distribution. |
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