# 1 or 2-way ANOVA on mean values from groups - allowed?

#### drkoch

##### New Member
Dear all,
We have just run a small experiment where we treated some animals with 2 compounds that are potential treatment for a disease which was induced through drinking water. The animals were assessed by a score from 0-3.

n=12 in each group that had the disease induced and only n=5 in the normal animals (no induction of disease or treatment).

We scored the animals at day 7 , 10, 14 and 21.

If I use a 2-way ANOVA on the all the data (from the attached dataset) there are no significant difference between the groups even though the mean values a lot lower in treatment 2 group (type 2 error?).

but if I use the 2way ANOVA on the mean score of each group (also in the dataset lower part), then it gets significant but is this allowed.

I also tried the 1way ANOVA on the mean values, which turns out significant. Is this a better way of describing the data?

I really hope that you can help me out as this is very important

Thank you very much for clarifying this so a regular t-test guy can understand this

View attachment 4155

#### noetsi

##### Fortran must die
I may not understand this correctly, but it looks like you assessed the animals (your DV) on a 4 point scale. ANOVA, like regression, requires an interval dependent variable and it is unlikely this will occur with just 4 levels.

Are you doing repeated measures ANOVA (which seems logical since you are tracking changes after an intervention)? I am also unclear when you shifted from two to one way ANOVA which variable you left out?

It might be you are using a more complex design than I am familiar with, if so I appologize for the confusion above.

#### drkoch

##### New Member
Thanks for the reply. I don't think that you are confusing. I'm the one not quite sure which method to use.
I've used Graphpad Prism to do my analyses and I'm also pretty sure that the ANOVA (repeated measures) are the correct way, but this I do not know whether Prism does that - but I guess so as one have to define how your data are acquired etc.

I also have STATA but I'm not familiar with it, so if you could guide me a bit towards the right direction on the above data I would be very happy...

#### MBJ

##### New Member
I think it is important that you decide if you are interested in a difference over time or just an overall effect of your treatments. The repeated measures can be very difficult to incorporate within a statistical model especially if they are not normally distributed. Furthermore, you dont get any more power if you are only intersted in the group differences.

I would suggest that you add (or take the average) of the scores of each animal and do a one way ANOVA on the results. If the residuals are not normally distributed (which is expected) use the Kruskal-wallis. I would also suggest that you take your control group out of the ANOVA if your research question is about the effect of the treatments on the disease.

Good luck

Morten

#### noetsi

##### Fortran must die
If your dependent variable has only 4 levels you can not use ANOVA or linear regression (the system you use will run it, but the results will be wrong).

#### drkoch

##### New Member
Hi again.
It right that the score is from 0-4. Then how do I test for statistical difference between the groups? I agree that the control group could just be left out as they only are used in the matter of the "normal" weight gain though out the study period.

I'll try to simplify the setup.

3 groups with 12 animal:

1st. group: vehicle
2nd group: compound 1
3rd group: compound 2

The score (0-4) is given at day 7, 10, 14, 21.

To test whether the compounds works they should be compared to the vehicle group.

Should I just pile the scores from all days into one and then compare it with 1w ANOVA or is there another way as noetsi suggests?

Thank you all. Your help means a lot

ps. if I calculate the average score for each group(x-axis) of each day (y-axis) like this:
View attachment 4158
and then use (data have non-gaussian distribution) the Kruskal-Wallis test - is that allowed?

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#### MBJ

##### New Member
I agree with noetsi that a 4 level dependent variable cannot make an ANOVA model. But the average could be a close enough approximation (although it theoretically cannot be normally distributed). The thing is, the effect size of a non-parametric test is often difficult to interpret since it is often made by ranking. Post hoc test are also limited in non-parametric tests.

If your dependent variable could be thought of as merely whole numbers from a scale the average and Kruskal wallis is a reasonable choice. If you want to do it the 'hard way' you can have a look at generalized estimating equations (GEE) but this is not trivial statistics.

Morten

#### drkoch

##### New Member
thanks, I've just added a small "ps" in the above tread - could you please comment on that?

#### MBJ

##### New Member
You should probably average for each animal instead. From looking at your data it seems that you have a problem with large variance in your second treatment group (some have only 1's and other all 3's). This makes it difficult to find any difference between groups although it seems that there is a numeric difference.

Morten

#### drkoch

##### New Member
I think you point at the exact problem. When I take the average for each animal it turns out insignificant probably due to the large variance. If I take the average for each group for each time point (7,10,14 and 21) there are too few data point for detecting whether it has a gaussian distribution but if I test the difference between vehicle vs. compound 2 then it turns out significant with both 1way ANOVA and and KruskalWallis test (and also using Holm-Sidak's/Dunn's multiple comparison, respectively).

Is this ok to do the analysis based on the average in the groups/day?

Best,

#### noetsi

##### Fortran must die
Hi again.
It right that the score is from 0-4. Then how do I test for statistical difference between the groups? I agree that the control group could just be left out as they only are used in the matter of the "normal" weight gain though out the study period.
If there is a logical ordering to the levels (which actually looks like five levels there) you can use ordered logistic regression. If they are not ordered you can use multinomial logistic regression. Note it does not matter how many levels the independent variable has. You can always make them dummy variables.

#### drkoch

##### New Member
One final question:

We have examined the animals at days 7, 10, 14, and 21. Are you allowed to pool the observations e.g. pool the data points for each day so that you end up with 3 groups with 48 observations (instead of 4 days with 12 observations) pr. treatment group and then use the 1w anova or kruskal wallis (if non-gaussian). In my mind this would be some kind of Overall effect based on the entire period?

Best,
L