My research project is on air pollution risk perception. I am testing/seeing if there are differences between perceptions of risk by its genre. Mental health, health, social, mechanistic, and a set of fake risks as control are the genre/type. To do so, I used a Likert scale from 1-10 for 28 risks, with the liberal option to reply 'I don't know' instead so respondent numbers differ per risk from 65-to-32. Giving respondents the choice to not subscribe to any scaled doubt or confidence means that respondent numbers for scaled answers differed from 65 for some questions to, at minimum, 32 for others.
(While inconvenient for the model the liberal option of 'don't know' prevents coercion into a doubt-confidence continuum, and it gives information for what individual risks that those sampled don't know enough about to guess versus those they do venture some confidence for.)
I grouped the risk responses into the five aforementioned classifications and summed or 'computed variable' them into the variables Mental Health, Health, Social, Mechanistic, Control in SPSS.
I also collected Tweets that associate each of the 28 risks with air pollution, with three control fake risks offering null results and some social risks null results, 0,0,0,0 over four weeks timeframe.
First method: the dependent variable was Likert-scale confidence. The Independent variable was risk-type. Risk type sub-groups were control, mental health, health, and social. Individual Likert-scale items are ordinal, but summed responses are interval so ANOVA is tenable (Carifio & Perla, 2008).
Tenable against classic objections of small-sample size and non-normal distribution (Norman, 2010); but what about variance inequality?
Stats tests run:
Wilko-Shapiro showed normal distributions with log10 transformation
Mauchly test showed sufficient sphericity with Greenhouse-Geissler correction
Repeated measures as same respondents entailed inter-dependencies
Homogeneity of variances was flouted
Hochberg post-hoc test is used as sample sizes are different for each (re)grouping
Second method:
Associative-Tweets results was dependent variable. The Independent variable was risk type. Risk type levels comprised control, mechanistic, social, health, and mental health.
Stats tests run:
All levels passed Muchaly's sphericity test.
Wilko-Shapiro normality test showed normal distribution for Health Risks and Mental Health Risks but not for fewer associated Mechanistic Risks, Social Risks, and Control Risks.
Homogeneity of variance was flouted
Different weeks weren’t substantial enough a variance to merit repeated measures
Hochberg post-hoc test was used as different sample sizes for grouped risks.
Should I do a Friedman Test or One Way ANOVA with caveats? Or something else, such as the one-way ANOVA with Welch and Games-Howell post-hoc test?
I’m new to this - and have dyscalculia - so guidance and explanation are appreciated.
Hello Edward,
Because of normality test is violated in some cases, you can use Friedman Test.
Best regards
If your outcome is a 1-10 rating you'll lose a lot of information with the Friedman test. Ideally one would use something like a multilevel ordinal logistic regression in this case. However, its possible you have summed scales (it isn't clear) in which case most researchers would use repeated measures ANOVA. This doesn't require homogeneity of variance as that's superseded by the sphericity assumption and the corrected tests already handle this.
A bigger issue would be missing outcome values. One solution would be to run a multilevel model (probably called a linear mixed model in SPSS). Else SPSS will likely just drop cases with missing data.
Also Carifio and Perla (2008) are incorrect to claim that ordinal variables are interval if summed. They might be better behaved, but they are still ordinal. A purer approach might be to run this as an ordinal SEM treating the risk category as a latent variable but that may be overkill in this context.
How is a "don't know" option liberal, and how often did respondents use it? Also, it sounds like your 28 risks are split into 5 categories. You might consider a confirmatory factor analysis model, which can be for "ordinal" data if that is what you believe these are. However, this depends on how often the "don't know" response is used.
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