I'm reviewing an analysis someone else has done on some Likert scale data. They've assigned each point on the scale 1-5 (1 = bad, 2 = poor etc.), found the average score in each area, and then converted to a percentage (by multiplying by 20) to give a percentage of total score (100% being the best, 20% being the worst).
I'm okay with this, but then they're computed a significance test as if the percentages were actual percentages, like if they'd gone out and asked people "Do you own your own home? Yes/ no". They've used a method similar to the one described here:
I want to tell them that this is a completely invalid way of analysing the data, and they've ignored the variance in the scores by collapsing everything into a percentage. I feel they should use ordinary t-tests on the data to determine significant difference. But I'm doubting myself. Any thoughts appreciated.