What test should i use? THESIS HELP!!

#1
Hi,

I am currently studying Zoology at university. I am currently in my final year conducting my dissertation. I have completed my data collection and I am now on to my statistics.
My dissertation looks at the relationship between light intensity and growth rate in marine sponges. I have 5 species of sponges and this was conducted over 7 weeks. I have 3 replicates of each species and once a week the area of the sponge was calculated. There were two light intensities; Light and Ambient. I was thinking is a 2-way ANOVA acceptable or should another test be used? I want to see if there is a significant difference between both light intensities, between species within the same intensity and between species within the different intensities

I hope that makes sense!

thankyou!
 
#2
A two-way repeated measures ANOVA should be appropriate for this problem, but I would also check to make sure the assumptions of ANOVA are met. To save time, I pulled them from a website.

  1. The populations from which the samples were obtained must be normally or approximately normally distributed.
  2. The samples must be independent.
  3. The variances of the populations must be equal.
  4. The groups must have the same sample size.
 
#3
A two-way repeated measures ANOVA should be appropriate for this problem, but I would also check to make sure the assumptions of ANOVA are met. To save time, I pulled them from a website.

  1. The populations from which the samples were obtained must be normally or approximately normally distributed.
  2. The samples must be independent.
  3. The variances of the populations must be equal.
  4. The groups must have the same sample size.
Yes it meets all the assumptions apart from being normally distributed...so a kruskall-wallis would be best?
thanks
 
#4
Kruskall-wallis is an alternative to anova, but you can also attempt to make your data normal by transforming it. Box-Cox transformations, log transformation...endless possibilities. But ANOVA also isn't extremely sensitive to deviations from normalcy. If it's not a huge deviation, ANOVA can still be trusted. It's worth trying a few test if you're unsure to see what their results are.

Hope this helps!
 

Karabiner

TS Contributor
#5
The populations from which the samples were obtained must be normally or approximately normally distributed.

Wrong. It's not the unconditional data, but the residuals which should be normally distributed,
but even this this only matters in case of small sample sizes.

The samples must be independent.

This makes no sense in case of repeated-measures ANOVA.
The variances of the populations must be equal.
Often this is true, but not always.
The groups must have the same sample size.
This is nonsense, I'm afraid.

Where is this strange list from?

With kind regards

Karabiner
 
#6
My apologies, I seem to have provided assumptions for non-repeated measures.

The concept of sphericity still holds when assessing variance (of the differences) equality among all combination of groups.

When you check normality it should be on the residuals and not your raw (unconditional) data.

Independence does not hold due to the nature of repeated measures.

Sample size is not a factor for repeated measures, but does hold for non-repeated.
 

noetsi

Fortran must die
#7
A couple of points

The formal tests of normality have well know problems, primarily a lack of power. A qq plot of the residuals is the better way to test this. Generally with high sample sizes non-normality is not that serious, although some argue this is not true if extreme outliers exist.

Variance is supposed to be homoscedastic. Graphs of residuals are commonly used to test this although I believe the Levene test is an alternative.

Samples don't have to have the same size, but if you do an unequal design problems can occur in certain circumstances (units drop out at different rates for example).

You have to control for internal and external threats to validity (not a formal assumption of ANOVA I think, but still a critical point in the analysis). Matching, random selection, a high enough sample size etc are all part of this.