# Is it possible to use ANOVA with a Likert Scale questionnaire?

#### Rose175

##### New Member
I am currently writing my dissertation and the deadline is getting close. I am really struggling with how to analyse my data - I had planned to do a one-way independent measures ANOVA but now I don't know how I will do it, and I've started to panic!

My study is investigating whether media footage of the 2010 London student protests (IV) can influence participants opinions (DV) of students and the police.

There are 3 Independent Variables i.e. 3 conditions (each with a different video).
And of course 1 Dependent Variable which is the opinion of each participant.

The participants have answered a 2 section questionnaire - one part before the video and one part after to see if their opinions changed. The Likert Scale has 6 items: Strongly Agree, Agree, Neither Agree Nor Disagree, Disagree, Strongly Disagree and Don't Know.

Would anyone be able to tell me whether I have chosen the correct analysis and how to enter my data into SPSS? Would I need to do separate analysis for each condition? Or even each participant? obviously I am aiming to find out whether any of the conditions influenced opinions and if any influence was positive or negative...

Thank you.

#### Lazar

##### Phineas Packard
There is not really enough info here. You do not tell us whether the likert DV is a scale score (an average of multiple items) or whether the DVs are single items.

#### trinker

##### ggplot2orBust
If there was would you open that can of worms

#### Lazar

##### Phineas Packard
Well the only thing I was thinking was that the range of possible values increases with scale scores and thus categorical approaches quickly become not feasible.

#### CB

##### Super Moderator
One of the many possible answers to this question is that it depends on your perspective on measurement, and the kind of inferences you want to make.

1) Perhaps you are an operationalist. You operationally define "opinions" as score on the questionnaire, and want only to make inferences about how the IV affects scores on the actual questionnaire. You are not interested in the question of whether the questionnaire is a reliable or valid measure of opinions; it's serving as your operational definition, and that's that. If this is your stance, you don't need to worry about "levels of measurement" or anything like that, although you should still check that the distributional assumptions of ANOVA are met (e.g., normality homoscedasticity and independence of errors).

2) On the other hand maybe you take a latent variable stance to measurement. You see your questionnaire as an imperfect measure of a latent variable (people's opinions) that exists out there in the real world, but which isn't directly observable. You consider that scores on your questionnaire are produced by a combination of variation in this latent variable, as well as measurement error. Because of the effects of measurement error, ANOVA is unlikely to produce particularly accurate inferences about the relationships between latent variables. If you are interested in inferences about latent variables, you will probably want to use a statistical method designed for making such inferences; e.g. structural equation modelling.

3) Finally, maybe you take a representationalist stance to measurement. You see your questionnaire scores as reflecting information about empirical relations observed amongst your sample. You don't want to have to make the ontological assumption that "opinions" exist out there in the world; measurement is just about summarising observed empirical relations. The implications of representationalism are probably the most complex. The whole idea of "levels of measurement" comes from representationalism.

From a representationalism perspective, the type of data you have means that you have observed ordinal relations. For example, if participant 1 ticks "agree" to an item, s/he has a higher level of agreement than someone who ticks "disagree"). However, you are not able to empirically compare differences between people. E.g. if participant 1 ticks "Agree" to an item, participant 2 ticks "disagree", and participant 3 ticks "strongly disagree", you can't empirically determine whether the difference between participant 1 and 2 is greater than, less than, or the same as the difference between participant 2 and 3.

Because you have only observed ordinal relations, a representationalist would argue that there are many possible ways to code responses to your items that are equally valid (as long as they are all monotonic transformations of each other). E.g. you could code response options like "strongly disagree", "disagree", "agree", and "strongly agree" as 1, 2, 3 and 4 respectively. This coding would convey the information that you have observed: E.g. that a participant responding "disagree" has a lower level of agreement than someone who ticks "agree". However, coding these 4 response categories as 1, 5, 7, and 1019 would be just as good: it again conveys the same information about the ordering of responses (1 < 5 < 7 < 1019).

Because the choice of coding scheme is arbitrary, within the set of all possible monotonic transformations, we would only want to use a statistical test that is invariant across all these transformations. This is not the case for ANOVA. If you coded responses to a Likert item as 1 (strongly disagree), 2 (disagree), 3 (agree) and 4 (strongly agree), and then used these responses as the response variable in an ANOVA, you would likely get quite different results than if you coded them as 1, 5, 7, and 1019. You could however use a Kruskal-Wallis test, which is a non-parametric rank-based alternative to ANOVA, which would not have this problem.