# Tag Info

33

Benefits of using the mean to summarise central tendency of a 5 point rating As @gung mentioned I think there are often very good reasons for taking the mean of a five-point item as an index of central tendency. I have already outlined these reasons here. To paraphrase: the mean is easy to calculate The mean is intuitive and well understood The ...

18

This response will discuss possible models from a measurement perspective, where we are given a set of observed (manifest) interrelated variables, or measures, whose shared variance is assumed to measure a well-identified but not directly observable construct (generally, in a reflective manner), which will be considered as a latent variable. If you are ...

17

Maybe too late but I add my answer anyway... It depends on what you intend to do with your data: If you are interested in showing that scores differ when considering different group of participants (gender, country, etc.), you may treat your scores as numeric values, provided they fulfill usual assumptions about variance (or shape) and sample size. If you ...

16

I'm going to argue from an applied perspective that the mean is often the best choice for summarising the central tendency of a Likert item. Specifically, I'm thinking of contexts such as student satisfaction surveys, market research scales, employee opinion surveys, personality test items, and many social science survey items. In such contexts, consumers ...

12

For basic summaries, I agree that reporting frequency tables and some indication about central tendency is fine. For inference, a recent article published in PARE discussed t- vs. MWW-test, Five-Point Likert Items: t test versus Mann-Whitney-Wilcoxon. For more elaborated treatment, I would recommend reading Agresti's review on ordered categorical variables: ...

12

I prefer to do power analyses beyond the basics by simulation. With precanned packages, I am never quite sure what assumptions are being made. Simulating for power is quite straight forward (and affordable) using R. decide what you think your data should look like and how you will analyze it write a function or set of expressions that will simulate the ...

12

To be somewhat technical here, those ratings aren't actually a Likert scale; they're just ordinal ratings. Now, having said that, your point is essentially correct. However, I often think too much is made of this issue. One thing to note is that it is typically understood that the average of a number of ordinal items can be approximately interval, and ...

11

Here is a quick attempt at heat map, I have used black cell borders to break up the cells, but perhaps the tiles should be separated more as in Glen_b's answer. library(ggplot2) runningcounts.df <- as.data.frame(table(importance, often)) ggplot(runningcounts.df, aes(importance, often)) + geom_tile(aes(fill = Freq), colour = "black") + ...

10

To add to @dmk38's response, "any set of scores gives a valid test, provided they are constructed without consulting the results of the experiment. If the set of scores is poor, in that it badly distorts a numerical scale that really does underlie the ordered classification, the test will not be sensitive. The scores should therefore embody the best insight ...

9

To manually verify the predictions derived from using polr() from package MASS, assume a situation with a categorical dependent variable $Y$ with ordered categories $1, \ldots, g, \ldots, k$ and predictors $X_{1}, \ldots, X_{j}, \ldots, X_{p}$. polr() assumes the proportional odds model  \text{logit}(p(Y \leqslant g)) = \ln \frac{p(Y \leqslant g)}{p(Y ...

9

The way I've done this is a bit of a fudge, but it could be fixed up easily enough. This is a modified version of the jittering approach. Removing the axes reduces the temptation to interpret the scale as continuous; drawing boxes around the jittered combinations emphasizes there's something like a "scale break" - that the intervals aren't necessarily ...

8

Conventional practice is to use the non-parametric statistics rank sum and mean rank to describe ordinal data. Here's how they work: Rank Sum assign a rank to each member in each group; e.g., suppose you are looking at goals for each player on two opposing football teams then rank each member on both teams from first to last; calculate rank sum by adding ...

8

Let's think about regular linear regression, and to make it concrete, let's say we are trying to predict height of people. When you regress heights against just an intercept term and no predictors, the intercept term will be be the height averaged over all the people in your sample. Lets call this term $\beta_0^{\text{no predictor}}$ Now, we want to add a ...

8

Here's an example of what a spineplot of the data would look like. I did this in Stata pretty quickly, but there's an R implementation. I think in R it should be just: spineplot(factor(often)~factor(importance)) The spineplot actually seems to be the default if you give R categorical variables: plot(factor(often)~factor(importance)) The fractional ...

7

There are major power and precision gains from treating Y as ordinal when appropriate. This arises from the much lower number of parameters in the model (by a factor of k where k is one less than the number of categories of Y). There are several ordinal models. The most commonly used are the proportional odds and continuation ratio ordinal logistic ...

7

Clason & Dormody discussed the issue of statistical testing for Lickert items (Analyzing data measured by individual Likert-type items). I think that a bootstraped test is ok when the two distributions look similar (bell shaped and equal variance). However, a test for categorical data (e.g. trend or Fisher test, or ordinal logistic regression) would be ...

7

It's commonplace to extract factor scores from ordinal-variable indicators. Researchers using likert measures do it all the time. Because factor scores are based on covariance, it's usually not that big a deal that the "intervals" might not be uniform within and across items, particularly if the items are comparable & use reasonably-compact scales (e.g., ...

7

Lets start with the good news: The proportional odds assumptions does not require that the distances between categories are the same. So what does the proportional odds assumption imply? Say we have three ordered outcomes (1, 2, 3), then we could model the choice of 1 versus 2 or 3 and the choice of 2 versus 3. The proportional odds assumption says that ...

6

The 'principled' approach (that is to say the a priori defensible approach that may not empirically make much difference) is to use a graded response model, a rather useful member of the IRT family often used for Likert type items. The R package ltm makes this very straightforward. You're then assuming there is a ordinal logistic regression relationship ...

6

The question (and your answer) invoke Stevens' theory of levels of measurement. This thread perhaps is not the place for a critical evaluation of that (old) theory, which has subsequently been found to be limited and counterproductive in many (but not all) applications. The question, though, implicitly suggests that this theory would provide a basis for ...

6

Concentrate on a few of the indexes right now. index.orig is the apparent predictive ability/accuracy score when you evaluate it on the data used to fit the model. index.corrected is the cross-validation-corrected version of the same index, i.e., corrected for overfitting (de-biased). Dxy is Somers' $D_{xy}$ rank correlation coefficient - a measure of ...

6

You're on the right track, but always have a look at the documentation of the software you're using to see what model is actually fit. Assume a situation with a categorical dependent variable $Y$ with ordered categories $1, \ldots, g, \ldots, k$ and predictors $X_{1}, \ldots, X_{j}, \ldots, X_{p}$. "In the wild", you can encounter three equivalent choices ...

5

Ordinal regression is not affected by empty cells of Y. Quantile grouping is not required unless you just want to reduce computational burden. Proportional odds or continuation ratio ordinal logistic models are likely to be able to handle the distribution of Y you plotted (with no grouping of Y).

5

The normality assumption is a convenient property of model's residuals, since it enables correct inferences about the estimated parameters and critical values of many other tests are also dependent on this assumption (therefore some corrections should be made, or you may roughly take more strict rule-of-thumb criteria, increasing the acceptable range of your ...

5

The proportional odds (PO) ordinal logistic model is a generalization of the Wilcoxon and Kruskal-Wallis tests, allowing for covariates, interactions, and anything else you can do in a regression model for a univariate response. A two-way ANOVA on ranks is not based on strong statistical principles. One of many computational tools for the PO model is the ...

5

The naive approach would be to compute the marginal distribution of rankings (e.g., mean score for each item), but it would throw away a lot of information as it does not account for the within-person relationship between ranks. As an extension to paired preference model (e.g., the Bradley-Terry model, described in Agresti's CDA pp. 436-439), there exist ...

5

The simple answer is that Likert scales are always ordinal. The intervals between positions on the scale are monotonic but never so well-defined as to be numerically uniform increments. That said, the distinction between ordinal and interval is based on the specific demands of the analysis being performed. Under special circumstances, you may be able to ...

5

You can start with Pearson's chi-squared test. It is implemented in R, as a function chisq.test. Here is the example with fictitious data: set.seed(1) #Generate some discrete variable y<-rpois(30,1) #Tabulate the values table(y) y 0 1 2 3 4 10 12 5 2 1 ##Calculate the theoretical probabilities of the values p<-dpois(0:3,1) ...

5

Welcome to the site, ellen. You can conduct contingency table analysis, and that can be done in two ways. First, you can tabulate the category against the occasion, which would give you a 2x4 table with 3 degrees of freedom, and test for independence of the counts. The test will tell you whether the marginal distributions of the response have changed ...

5

A spineplot (mosaic plot) works well for the example data here, but can be difficult to read or interpret if some combinations of categories are rare or don't exist. Naturally it's reasonable, and expected, that a low frequency is represented by a small tile, and zero by no tile at all, but the psychological difficulty can remain. It's also natural that ...

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