Discrete, or ordinal, data have a rank order, but the scale is not necessarily linear. A pain scale from 1 to 10 is a good example; a pain score of 8 is not necessarily twice as bad as 4.
Examples of categorical, or nominal, data are colour or shape. The data are different, but no rank order exists. The test chosen to analyse the data is based on the type of data collected and some key properties of that data Hoskin, undated. In More Good Reasons to Look at the Data, we looked at data distributions to assess centre, shape and spread and described how the validity of many statistical procedures relies on an assumption of approximate normality Niedeen et al, But what do we do if our data are not normal?
Nonparametric procedures are one possible solution to handle non-normal data. He stated the conditions to include; the observations must be independent, the observations must be drawn from normally distributed populations, these populations must have the same variances and variables involved must have been measured in at least an interval scale.
An r value of 1. An r of zero means that the 2 variables are completely random. The important thing to remember is that this is only an association and does not imply a cause- and-effect relationship. It was developed by a statistician working at the Guinness brewery and is called the Student t-test because of proprietary rights.
A single sample t-test is used to determine whether the mean of a sample is different from a known average. A 2-sample t-test is used to establish whether a difference occurs between the means of 2 similar data sets. The t-test uses the mean, standard deviation, and number of samples to calculate the test statistic. In a data set with a large number of samples, the critical value for the Student t-test is 1.
The calculation to determine the t-value is relatively simple, but it can be found easily on-line or in any elementary statistics book.
However, with the z-test, the variance of the standard population, rather than the standard deviation of the study groups, is used to obtain the z-test statistic. Using the z-chart, like the t-table, we see what percentage of the standard population is outside the mean of the sample population. As some assumption of sample size exists in the calculation of the z-test, it should not be used if sample size is less than If both the n and the standard deviation of both groups are known, a two sample t-test is best.
The test statistic is then used to determine whether groups of data are the same or different. When hypothesis testing is being performed with ANOVA, the null hypothesis is stated such that all groups are the same. As with the t- and z-statistics, the F-statistic is compared with a table to determine whether it is greater than the critical value.
In interpreting the F-statistic, the degrees of freedom for both the numerator and the denominator are required. The degrees of freedom in the numerator are the number of groups minus 1, and the degrees of freedom in the denominator are the number of data points minus the number of group. According to Robson , non-parametric tests should be used when testing nominal or ordinal variables and when the assumptions of parametric test have not been met A non-parametric statistical test is also a test whose model does NOT specify conditions about the parameters of the population from which the sample was drawn.
It does not require measurement as strong as that required for the parametric tests. Most non-parametric tests apply to data in an ordinal scale, and some apply to data in nominal scale. The chi-square test helps to decide whether a frequency distribution could be the result of a definite cause or just chance. It does this by comparing the actual distribution with the distribution which could be expected if chance was the only factor operating.
If the difference between the observed results and the expected results is small then perhaps chance is the only factor. On the other hand if the difference between observed and expected results is large, then the difference is said to be significant and we expect that something is causing it.
The difference is that the data need not be linear. To start, it is easiest to graph all the data points and find the x and y values. Then rank each x and y value in order of occurrence. Similar to the Pearson correlation coefficient, the test statistic is from -1 to 1, with -1 being a perfect negative correlation and 1 a perfect positive correlation.
It is analogous to the t-test for continuous variable but can be used for ordinal data. This test compares 2 independent populations to determine whether they are different.
The sample values from both sets of data are ranked together. Once the 2 test statistics are calculated, the smaller one is used to determine significance. Unlike the previous tests, the null hypothesis is rejected if the test statistic is less than the critical value. The U-value table is not as widely available as the previous tables, but most statistic software will give a p-value and state whether statistical difference exists.
This test, like the previous example, ranks all data from the groups into 1 rank order and individually sums the different ranks from the individual groups. These values are then placed into a larger formula that computes an H-value for the test statistic. Chapter 16 - Non-parametric statistics. Chapter 16 - Non-parametric statistics Try the following multiple choice questions, which include those exclusive to the website, to test your knowledge of this chapter.
Once you have completed the test, click on 'Submit Answers for Grading' to get your results. This activity contains 20 questions. Parametric Equations Quiz. This quiz tests the work covered in Lecture 20 and corresponds to Section 4. There are more web quizzes at Wiley, select Section 8.
Types of Tests. Nonparametric tests include numerous methods and models. Below are the most common tests and their corresponding parametric counterparts: 1. Mann-Whitney U Test. The Mann-Whitney U Test is a nonparametric version of the independent samples t-test. The test primarily deals with two independent samples that contain ordinal data.
Questions 19 - 21 Match each of the Nonparametric procedures presented on the left with the corresponding experimental design from the list on the right use each alternative only once. Kruskal-Wallis H Test a two independent samples.
Nonparametric Test - an overview ScienceDirect Topics. There is a nonparametric test available for comparing median values from two independent groups where an assumption of normality is not justified, the Mann-Whitney U-test. The null hypothesis for this test is that there is no difference between the median values for the two groups of observations.
As for all nonparametric tests the test statistic is calculated after ranking the observations. Applied Biostatistics: Questions and Answers. Applied Biostatistics: Questions and Answers There was not time to do non-parametric methods. In large samples, you would get the same answers as the z test and chi-squared tests.
In SPSS, there is no separate z test. We have to use the t test with unequal variances, which does the same calculation and gives the same answer. PDF The t-test. On the other hand, if participants read the test items carefully, they might be able to reject certain answers as unlikely regardless of what the passage said.
Statistical tests fall into two kinds: parametric tests assume that the data on which they are used possess certain characteristics, or "parameters". If the data do not possess these features, then the results of the test may be invalid. The parameters which are taken for granted are:.
Statistics Nonparametric and Robust Methods. Chapter 1 pdf Mathematical preliminaries. Chapter 3 html The randomization model. Comparing two treatments in the randomization model. Permutation test, Fisher's exact test. Chapter 4 html. The paired t-test assumes that the population standard deviation of paired differences is unknown and will be estimated by the data. The nonparametric analog of the t -test is the Wilcoxon Signed-Rank Test and may be used when the one-sample t-test assumptions are violated.
A fisheries researcher wishes to test for a difference in mean weights of a single species of fish caught by fishermen in three different lakes in Nova Scotia.
The significance level for the test will be 0. The test is a worthless test, since it gives errors when detecting both sick and healthy subjects. A regression line is a straight line which:.
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