# Sample size question, 7 samples with different sample sizes

I am looking at the measurements of different organisms (in nanometers).

I have 7 different populations. 1 is what I know the origins of, and I want to compare the size of this to my other 6 populations, which I do not yet know the origins of. I want to compare both width and length (so I have 14 columns on SPSS).

The issue is, all of the sample sizes are different. One population is 3400, and the others barely touch 60 but vary. Would it be okay to randomly generate a population of the 3400 of around 60 using a number generator?

Regarding comparing the rest, is an ANOVA okay to assess size difference within and between the groups? I have to use SPSS.

Thanks so so much in advance. My supervisor has proclaimed he is "not a statistician", so I'm pretty desperate for help!

I want to compare both width and length (so I have 14 columns on SPSS).

Do you have paired data (Repeated measures of the same population)?

Regarding comparing the rest, is an ANOVA okay to assess size difference within and between the groups? I have to use SPSS.

ANOVA is appropriate to assess size differences between the groups, but make sure that the assumptions of ANOVA are fulfilled. Specifically, that your samples are normally distributed, and that they don't violate the assumption of homogeneity of variances.

A MANOVA can also be used, since you have more than one dependent variable (length and width). For an ANOVA, you would have to run the test for each variable at a time, since it's a univariate test. For the MANOVA, you can test all variables at once, since it's a multivariate analysis. Another option is to sum the variables for width and length and have a sumscore called "size", which you can then run ANOVA on. This might not be as accurate as width and length, but if "size" is really the variable you want to look at, that could be an option.

To run an ANOVA in SPSS with 2 or more groups, do the following:

click Analyze -> Compare Means -> One-Way Anova...

Add your dependent variable to the "dependent" box and your group variable to the "factor" box. Under "options" check the "Homogeneity of variance test" box. This will give you Levene's test of homogeneity in the output. If Levene's p-value is not significant, than your samples do not have a significantly unequal variance from each other, and you are ok. This assumption is violated if p < 0.05 (or your chosen significance level).

You can also enter the "Post Hoc..." options and check on Bonferroni (for a more strict) and/or Tukey (for the more common) Post Hoc Test. ANOVA only tells you whether one or more of the groups were significantly different from the rest, not exactly which ones differ from each other. The Post Hoc test is used to find out which groups are significantly different from each other when you already know at least one are significantly different from your ANOVA.

Normality can be tested under Analyze -> Explore -> "Plots..." and check the "Normality plots with tests" option. all of the groups need to follow the normal distribution, and like Levene's test, the assumption of normality is violated if p < 0.05 in your normality test (Shapiro-Wilk is generally preferred).

MANOVA is run similarly in SPSS. Analyze -> General linear model -> Multivariate...

Here you can add all your dependent variables in the "dependent" list.

The issue is, all of the sample sizes are different. the 1 bacteria population is 3400, and the others barely touch 60 but vary. Would it be okay to randomly generate a population of the 3400 of around 60 using a number generator?

ANOVA does not assume that the sample sizes are equal. As long as all the samples have a solid sample size, your study should be fine even though one sample is drastically larger than the others. You shouldn't need to randomly generate a population.

• Hello Ederi..I can't quite tell you just how helpful that response was - thank you so much for explaining that so well! It is not a paired test. I have one measurement of lengths for all samples, and one measurements of width of all samples. I want to compare the lengths to eachother, and the widths to other widths.. I followed your instructions and my Levene result was highly significant (.000). Does this mean I need to do a Kruskal Wallis test? The distribution of all populations are normal. I did a Tukey and got the results I would predict by looking at my figures, so this is a shame! – carley Dec 28 '15 at 19:47
• The Welch and Brown-Forsythe has thrown out a .000 too. If I have to do a non-parametric ANOVA, is there an alternative to the Tukey test? Also, can a non-parametric ANOVA handle these highly unequal sample sizes? – carley Dec 28 '15 at 20:23
• If you do not have paired data, then why do you have 14 variables (columns)? How is your dataset organized? If this is a two-sample dataset, it should look something like this: docs.google.com/spreadsheets/d/… I've given permission to change the google excel file if you'd like to show how its put up. – Ederi Jan 4 '16 at 9:06
• "I did a Tukey and got the results I would predict by looking at my figures, so this is a shame!": It's always a good thing to have numbers to back up what is assumed in figures. Your interpretation of Levene's p-value is correct, and yes you should use Kruskal Wallis. Assuming you have set up your data correctly. And a non-parametric alternative to ANOVA can also handle highly unequal sample sizes. – Ederi Jan 4 '16 at 9:07
• Hello again, I have edited the sheet to show you what I am working with. After reading a lot I think I have made progress, though I am not 100% sure I am correct. I have analysed both width and lengths separately, as a non-parametric MANOVA was either non-existent or beyond the scope of the stats I have learned. I have done a Kruskal Wallis test and a post-hoc to look for the differences between my lengths, and a separate Kruskal Wallis and post-hoc on my widths and I have some sig. differences and non-sig too. Sorry, my 14 columns were my dataset prior to organising it for analysis. – carley Jan 4 '16 at 17:23