# Longitudinal relationship between chocolate consumption and happiness: repeated measures ANOVA?

I am using SPSS and having some trouble with a research question which is analogous to the hypothetical question:

Is there a longitudinal Relationship between Happiness and Chocolate Consumption?

Let’s say I take a sample of people and contact them when they are aged 14 and aged 18 and ask them: a) What is your chocolate consumption in grams per day. b) Are you happy?

I have my fictitious data in the following wide format:

ID HAPPY.14 HAPPY.18 CHOC.14 CHOC.18

1 YES YES 100 5

2 YES NO 50 30

3 NO YES 30 50 etc.

I would like to know if the mean chocolate consumption per day is higher among happy people than those who are not happy while accounting for the fact that I have taken repeated measures of both chocolate and happiness at the two time points.

Approach 1

I suppose one way of doing this would be to do an ANCOVA, using time (before/after) as a grouping variable and controlling for happiness status. However, I think this may be inadvisable as correlation between the two time points would be neglected.

Approach 2

I understand that one valid approach for this should be a repeated measures ANOVA. I’m just not sure how to do this correctly in SPSS. I have specified my within-subjects factor as chocolate consumption with age 14 data as level one and age 18 data as level 2. What I’m uncertain about is the next step – specifying covariates and between individual factors – I have the option of adding HAPPY.14 and OR HAPPY.18 as a between individual factor. If I add both the output tells me about the effect of HAPPY.14 and HAPPY.18 as you’d expect, not about the “effect” of happy (YES/NO)per se.

I realise it’s a basic question. Any feedback would on either of the two approached would be greatly appreciated.

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You may need to clarify what you mean by

"accounting for the fact that I have taken repeated measures..."

You say that

"I would like to know if the mean chocolate consumption per day is higher among happy people than those who are not happy..."

This suggests to me that time is not really relevant to your research question. Thus, you could do one of the following.

1. You could correlate mean happiness ([time1 + time2] / 2) with mean chocolate consumption.
2. You could correlate happiness with chocolate consumption at a given time point.
3. You could correlate happiness with chocolate consumption across times (e.g., 1 with 2).

A variant on the above would involve performing a regression or other predictive model predicting one variable from the other.

Alternatively, you may find that you can rephrase your research question more clearly to incorporate what you are interested in with regards to the effect of time.

• You could correlate chocolate change scores with happiness change scores.
• You could predict time 2 chocolate from time 1 chocolate and time 1 happiness to see whether time 1 happiness predicts over and above time 1 chocolate.

As a side point, while it may be an artificial example, it seems strange to measure happiness as a Yes / No variable. I would measure it as a scale. It is also a little strange talking about the mean of a Yes / No variable.

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You may think about happiness as the dependent variable, and you could use logistic regression with chocolate consumption as a predictor. Some people may be generally happier or less happy independently from chocolate consumption. This can be modelled by including subject id as a random effect categorical predictor. Age might also influence happiness. After these the model would look like this: logit(happy) ~ choc + age + id, where age is either 14 or 18, and the data are in the long format, a mixed effect logistic regression including a random categorical, a fixed categorical and a continuous predictor. (As an analogue of the repeated measures approach you could use a covariance pattern model, where id is not a predictor, but used in the specification of the covariance.)
Alternatively chocolate consumption can be regarded as dependent variable. choc ~ happy + age + id could be the model (long data format), where id is a random effect, mixed effect ANOVA; or choc ~ happy + age, where repeated measures are considered, repeated measures ANOVA.