Let me suggest that whether you use ANOVA for Likert scale items depends on your general attitude towards averaging Likert scale items. There's a great New Yorker cartoon that shows a road side sign for a town, let's call it New Bedford. On the sign announcing the town, it proclaims:. I liked the cartoon so much that I paid to have it included in my book on the chapter on meta-analysis. But the general concept also applies here.
There are some things that were not meant to be totaled or equivalently, some things that were not meant to be averaged. If you average a Likert scale, you are making the presumption that a score of 1 combined with a score of 5 is equivalent to two scores of 3.
In other words, a "strongly agree" and a "strongly disagree" provides the same average impression as two "neutrals".
If the shapes and spreads of the distributions are approximately the same, the Kruskal-Wallis test functions as a test for difference between the group locations. Although the Mann-Whitney test can be used where there are only two groups as a nonparametric analogue of a t -test, we present the Kruskal-Wallis test as having the broadest application because it can deal with designs involving two groups as well as those with more than two groups.
Given numerical data in k groups, the logic of the Kruskal-Wallis test considers the number of cases in each group that fall above or below the common median i. If there is no difference between the groups, we expect approximately half of the observations in each group to fall above the common median and approximately half to fall below the common median.
The Kruskal-Wallis test statistic, H , rises as the data deviate from these expectations. If the deviation is sufficiently great, we conclude that the different groups do not all come from the same population. The Kruskal-Wallis test proceeds as follows. Calculation of ranks. For ties equal observations , the rank is the mean of the ranks that would have applied if the observations had differed slightly.
If the underlying data are true numerical observations measurement or ratio scale , there are usually few ties and the adjustment for ties makes little difference. However, in ordinal data the number of distinct values is usually limited, and ties are common.
Thus, for ordinal data, the adjustment for ties may be quite important. A significant result in a Kruskal-Wallis test indicates that not all the treatment groups come from the same population, but it will not indicate which groups are significantly different from others. If H is significant, post hoc testing can be used to determine which groups are significantly different from others in a series of tests between pairs of groups, analogous to similar approaches in ANOVA.
Such multiple pairwise tests increase the likelihood of spuriously finding a significant result for a detailed exposition, see Field et al. Thus, depending on the software package used, these tests may or may not include corrections for multiple comparisons such as the Bonferroni correction or the sequential Bonferroni correction often favored because the Bonferroni correction is deemed too severe; Holm, Consider a fictitious example from plant pathology, a field in which ordinal scales are often used for assessing the severity of disease.
The tomato blight fungus infects plants via the leaves and spreads through the vascular tissue, weakening the plant and ultimately killing it. Fungicides administered as foliar sprays treat the disease, but the dose is critical — too low a dose has little protective effect, while too high a dose is toxic to the tomato plant.
An experiment is designed in which 50 tomato plants are infected with tomato blight and then assigned at random to one of five dose levels of fungicide. The response of the plants is assessed on a five-point rating scale, so the data are ordinal and unsuited to a parametric test Table 1. If commercial software is unavailable and R is unsuitable because of the need to learn coding, freeware with a graphical user interface can be used.
Selecting the Kruskal-Wallis tab in the output gives the H statistic with and without correction for tied ranks but PAST does not display the degrees of freedom, calculated simply as one less than the number of groups; Figure 1. In this example the groups all have identical sample sizes, but this need not be the case and PAST will accept unequal group sizes.
The treatments lead to significant differences in survivorship. PAST also offers post hoc pairwise comparison of treatments using Mann-Whitney tests Figure 2 , with options for adjusting these with a Bonferroni correction or sequential Bonferroni correction.
For a more detailed version of these instructions, see Appendix S1 available as Supplemental Material with the online version of this article. There are options for entering data directly online or copying and pasting from Excel, with a maximum of five groups available. In this example the groups all have identical sample sizes, but this need not be the case and VassarStats will accept unequal group sizes.
The output includes a display of the ranks calculated from the raw data and the H statistic with degrees of freedom, but not H corrected for ties Figure 3.
There is no provision for post hoc pairwise testing, although this could be done by selecting the option for Mann-Whitney tests and analyzing each paired combination individually. Bonferroni or sequential Bonferroni corrections would need to be applied manually. This shows an increase in ranks from treatment A to treatment D, with a fall in treatment E. But they are also sometimes exactly what you need.
Another model-based approach combines the advantages of ordinal logistic regression and the simplicity of rank-based non-parametrics. The basic idea is a rank transformation: transform each ordinal outcome score into the rank of that score and run your regression, two-way ANOVA, or other model on those ranks. The thing to remember though, is that all results need to be interpreted in terms of the ranks. Just as a log transformation on a dependent variable puts all the means and coefficients on a log DV scale, the rank transformation puts everything on a rank scale.
Your interpretations are going to be about mean ranks, not means. I have two categorical variables which are ordinal, what is the best way to analyze my data either using ordinal logistic regression for each of the dependent variable or any one model to use in combination?
Your email address will not be published. Skip to primary navigation Skip to main content Skip to primary sidebar There are not a lot of statistical methods designed just for ordinal variables. Some are better than others, but it depends on the situation and research questions. Treat ordinal variables as nominal Ordinal variables are fundamentally categorical.
Non-parametric tests Some good news: there are other options. For example, you can use the post hoc test to determine whether pain score is statistically significantly different between Drug A and Drug B. We do this using the Harvard and APA styles. Remember, the distribution of your data will determine whether you can report differences with respect to medians. In our enhanced guide, not only do we explain how to test for this assumption, but we also show you how to interpret and report the results whether you pass this assumption or not.
You can learn more about our enhanced content on our Features: Overview page. Kruskal-Wallis H Test using SPSS Statistics Introduction The Kruskal-Wallis H test sometimes also called the "one-way ANOVA on ranks" is a rank-based nonparametric test that can be used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable.
SPSS Statistics Assumptions When you choose to analyse your data using a Kruskal-Wallis H test, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a Kruskal-Wallis H test. Examples of ordinal variables include Likert scales e.
Examples of continuous variables include revision time measured in hours , intelligence measured using IQ score , exam performance measured from 0 to , weight measured in kg , and so forth. You can learn more about ordinal and continuous variables in our article: Types of Variable. Assumption 2: Your independent variable should consist of two or more categorical , independent groups. Typically, a Kruskal-Wallis H test is used when you have three or more categorical, independent groups, but it can be used for just two groups i.
Example independent variables that meet this criterion include ethnicity e. Assumption 3: You should have independence of observations , which means that there is no relationship between the observations in each group or between the groups themselves. For example, there must be different participants in each group with no participant being in more than one group. This is more of a study design issue than something you can test for, but it is an important assumption of the Kruskal-Wallis H test.
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