Which t test to use, is it even applicable?

#1
Hi,

I have a sample of men and women based on their age (21,....76) and I have their willingness (yes, no, not sure/1,2,3). I want to see if the age affects the willingness, or if age shows a significant effect/association with willingness.
Is an independent t test applicable here?
Which statistical test could I use?

Thanks!
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Not sure your purpose, but null hypothesis testing is over used in these scenarios. Just make three stacked histograms of age by Willingness status. You can also put boxplots under the histograms if you want. This should give you tangible visual information.

1634665115704.png
 
#3
Not sure your purpose, but null hypothesis testing is over used in these scenarios. Just make three stacked histograms of age by Willingness status. You can also put boxplots under the histograms if you want. This should give you tangible visual information.

View attachment 3720
My purpose is to see if any age in particular is more/less willing to opt for something. Do you think perhaps a chi-square test would be better suited, since I can treat age as category in that case. An independent t-test was used for this originally, but I am struggling to see if it's relevant since age is a continuous variable, and willingness is a categorical.
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
Have you done the histogram, yet?

What is your dependent variable? Willingness. So it is willingness explained by age. This would result in a multinomial logistic regression, but you need to visualize it first with histograms to see what the relationship looks like. If it is bimodal, you may want to use age as a spline term in the model. Chi-Sq test robs you of information since age in inherently a continuous variable and not a category.
 

Karabiner

TS Contributor
#5
Start with plots, as hlsmith suggested. If you need a statistical test, you could
consider Spearman rank correlation (to see if there is a monotonous association),
or oneway analysis of variance with willingness as grouping variable and age
as (technically) the dependent variable. If your sample zize is small, you could
consider Kruskal-Wallis H-test.

With kind regards

Karabiner
 

noetsi

No cake for spunky
#6
Whether you can use a t test with likert data is much in dispute to answer the original question. It depends on if you can assume the distances between the intervals are the same in part. It is more likely to be reasonable with 5 (some say 7) or more levels. T test assume interval data which likert data is not, but some argue it is interval like especially with enough levels. There is no agreement on this issue.