I am conducting a small research into the adoption of smart home technologies for elderly people. In this research I have conducted both questionnaires and interviews, with the questionnaire being conducted among people who were interviewed. In total 11 people were interviewed and so 11 responses were obtained for the questionnaire.
Currently I am trying to analyze the questionnaire, I am, however, a little bit stuck so maybe you can provide us with some advice.
In my questionnaire I am aiming to measure both loneliness and the health status of elderly people. These variables are measured through 3 and 6 five point Likert scales (strongly disagree – disagree – neutral – agree – strongly agree) respectively. Now that I have got the questionnaire results, I'd like aggregate the different Likert scales, measuring the same concept, into one score that represents the concept, in order to be able to compare participants on their scores.
I, however, have no clue how to do this. What I do know is that averaging the scores composing one scale is not reliable as the data is ordinal. Furthermore, median and modes do not make sense either as the number of statements is too low for them to be valuable. Simply adding the scores might be a solution, though I have the feeling that this is not entirely correct due to the possible implied intervals that are suggested by this method.
Do you have any advice on how to best calculate a composite score for each of the two scales consisting of 3 and 6 items respectively?
Best Answer
There are two ways you can take: (1) just use the sums of scores, (2) use an Item Response Theory (IRT) based method. Using sums of raw scores is very common in social sciences but many psychometricians do not consider it being a sound approach. If you sum up the different questions from the questionnaire you assume that every answer provides you with the same amount of information - and in the real life that is not true. However, your data provides you in information on both the "abilities" of your responders and on precision of your questions, so that you can use both sources of information to gain deeper understanding of both your questionnaire and your responders. This is a pretty wide topic so you can check different resources on this topic, e.g. here, here or in this book. IRT will let you to use your data to obtain information on latent features measured by the questionnaires on continuous $Normal(0, 1)$ scale, so it also makes life easier with further analysis. It is mostly used in the area of educational research, so don't get discouraged that most examples in the books and articles are on measuring student abilities, because the method could be used for analyzing any kind of test or questionnaire data to obtain the latent profiles of the responders.
There are many statistical packages for IRT, for example, in R you can use mirt or ltm.