Suitability of non-parametric tests.

Valmont

Hi everyone, I hope you could clarify an issue I'm having with my statistical analysis at the moment.

The scores for one of my DVs is not normally distributed (by a long shot) and homogeneity of variance is not assumed (according to the Levene's test). Considering I have absolutely no idea how to do the relevant transformations on the data, should I go ahead with a non-parametric Kruskal- Wallis test?

The data for my other DV is normally distributed but homogeneity of variance is not assumed, are there any adjustments or alternative post-hoc tests I should run seeing as this assumption is not met?

Thanks in advance.

2Scoops

Valmont wrote: »

Hi everyone, I hope you could clarify an issue I'm having with my statistical analysis at the moment.

The scores for one of my DVs is not normally distributed (by a long shot) and homogeneity of variance is not assumed (according to the Levene's test). Considering I have absolutely no idea how to do the relevant transformations on the data, should I go ahead with a non-parametric Kruskal- Wallis test?

The data for my other DV is normally distributed but homogeneity of variance is not assumed, are there any adjustments or alternative post-hoc tests I should run seeing as this assumption is not met?

Thanks in advance.

Kruskal-Wallis will work for both DVs, no assumptions necessary. ANOVA is usually quite robust to violations of homogeneity of variance. A log transformation will normalize most data: just log the values.

Valmont

I added 3 new cases of data that I hadn't scored yet and now I have both normality and homogeneity of variance for one D.V. Is it ok to do an ANOVA for one DV (I have to as the post-hoc contains the interesting part of my project) and a kruskal wallis for another one? I'm reluctant to run a non-parametric analysis but if I have to I will.

What transformation would be ok for data skewed incredibly to the right (basically scores out of 10 and out of 34 cases, none got lower than 8) without homogeneity of variance? Thanks.

2Scoops

Valmont wrote: »

I added 3 new cases of data that I hadn't scored yet and now I have both normality and homogeneity of variance for one D.V. Is it ok to do an ANOVA for one DV (I have to as the post-hoc contains the interesting part of my project) and a kruskal wallis for another one? I'm reluctant to run a non-parametric analysis but if I have to I will.

You can do post-hocs following non-parametric analyses, too; an ANOVA is not strictly necessary for that. There is no real reason to avoid non-parametric tests unless you feel power might be an issue. It's perfectly fine to run one of each, IMO, but your reviewer/marker might ask you about it. Be prepared to explain why you chose to run 2 different tests rather than normalize or just use non-parametric.

Valmont wrote: »

What transformation would be ok for data skewed incredibly to the right (basically scores out of 10 and out of 34 cases, none got lower than 8) without homogeneity of variance? Thanks.

Well, is it still normally distributed, just not around '5?' Check the skewness/kurtosis values - you may not have a problem! Otherwise, I usually go with Log - it's common enough not to raise eyebrows. I'm sure there are better transformations out there, though...

Valmont

2Scoops wrote: »

but your reviewer/marker might ask you about it. Be prepared to explain why you chose to run 2 different tests rather than normalize or just use non-parametric.

That's why I asked they did question me about it. Thanks for the advice I'll defintiely transform the data now.

Valmont

Ok I'm almost there. I found out how to log transform my data but my data is negatively skewed and now I need to reflect my data (multiply by -1?) add a constant (I have no idea what this means), this then should reverse the distribution so that I can run the log transformation, and then I have to reflect it back again....

Any ideas how I can run this reflect in SPSS? If not is there a simple formulat for it?

2Scoops

You can't log zero or a negative value. You need to add a multiply by -1 (and add a constant value, if necessary) so that all the values are positive and non-zero.

Valmont

2Scoops wrote: »

You need to add a multiply by -1 (and add a constant value, if necessary) so that all the values are positive and non-zero.

I multiplied all my scores by -1 and now my data is positively skewed so I can run the log. How do I get the data to be positive whilst retaining the positively skewed distribution? Is this where I add a constant? I'm not sure what this is or how to do it?

Valmont

I added the same value to all my data so that they would be greater than 0 but after I ran the log again and square root transformation the data is still not normally distributed. I might just have to gloss over the issue. Thanks for the help.

2Scoops

How are you assessing normality?

Remember you could just use 2 non-parametric tests, as well.

Valmont

2Scoops wrote: »

How are you assessing normality?

Remember you could just use 2 non-parametric tests, as well.

An informal inspection of the histograms for each group with the normality line superimposed but I've mainly been going by the Shapiro-Wilks goodness of fit test. My supervisor and lecturers strongly advised against running two non-parametric tests.

Of my two D.V's the one that meets the assumptions of the ANOVA is the most important one as I have found significance and the other one was not so revealing at all as most cases were more or less similar, so similar that the data was completely skewed to the right, it still has the characteristic normal curve bend though.

2Scoops

Valmont wrote: »

My supervisor and lecturers strongly advised against running two non-parametric tests.

Did they explain why? Just curious. Either way, just agree with them - they have the powah in this situation. :pac:

Valmont wrote: »

Of my two D.V's the one that meets the assumptions of the ANOVA is the most important one as I have found significance and the other one was not so revealing at all as most cases were more or less similar, so similar that the data was completely skewed to the right, it still has the characteristic normal curve bend though.

It's odd that a transformation has not normalized it. I don't live or die by Shapiro-Wilk myself. Check if skewness/kurtosis are within 2 z-scores. Try a few other normalization methods and see if they work. If not, maybe run it both ways (parametric and non-parametric) but then present only the parametric data. If they ask for more detail or try to catch you on normality, say the non-parametric test was consistent in its findings (assuming it is!) - problem solved. MANOVA is also an option.

Valmont

2Scoops wrote: »

Did they explain why? Just curious. Either way, just agree with them - they have the powah in this situation. :pac:



It's odd that a transformation has not normalized it. I don't live or die by Shapiro-Wilk myself. Check if skewness/kurtosis are within 2 z-scores. Try a few other normalization methods and see if they work. If not, maybe run it both ways (parametric and non-parametric) but then present only the parametric data. If they ask for more detail or try to catch you on normality, say the non-parametric test was consistent in its findings (assuming it is!) - problem solved. MANOVA is also an option.

The skewness and kurtosis values are all lower than -1.5, lower as in closer to zero. Would it be kosher to mention in my results section that "non-parametric analysis revealed consistent/similar results" ?

2Scoops

Valmont wrote: »

The skewness and kurtosis values are all lower than -1.5, lower as in closer to zero. Would it be kosher to mention in my results section that "non-parametric analysis revealed consistent/similar results" ?

It would only make sense to mention that non-parametric analyses were consistent if there was some question of the assumptions of the parametric test being violated. It sounds to me like the distributions are perfectly normal; false positive by Shapiro Wilk, which often happens with a large sample size.

Valmont

2Scoops wrote: »

It sounds to me like the distributions are perfectly normal; false positive by Shapiro Wilk, which often happens with a large sample size.

Ok I might just include my skewness and kurtosis values as a demonstration of normality as my total N= 34 with four groups having N=8, N=8, N=8, N=10, respectively. Regarding the violation of homogeneity of variance, what can I do? Is it incorrect to run an ANOVA when this is the only assumption violated? I've read that the ANOVA is robust to violations.

2Scoops

Valmont wrote: »

Regarding the violation of homogeneity of variance, what can I do? Is it incorrect to run an ANOVA when this is the only assumption violated? I've read that the ANOVA is robust to violations.

ANOVA is generally robust to this violation, provided the it has not been violated by much. Depending on your statistic, it may provide an adjusted p-value where homogeneity of variance has not been assumed. Alternatively, bust out the consistency between parametric/non-parametric results.