Hi Mr. Mohammed ALi Alawi,

sure you can perform a Kruskal-Wallis test (test whether the median is the same in every group) and this is a no-parametric test.

Also The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test, t-test for matched pairs, or the t-test for dependent samples when the population cannot be assumed to be normally distributed.

I'm not a SPSS user. Then I can't answer at the last question.

Quite difficult to answer your question without knowing exactly what sort of data data you have.

1) If you want to compare the mean, then you should have presumably measured the number of +ve and -ve bacteria from a large number of eggs? As long as you have sufficient number of eggs measured (there's no right or wrong answer in how many will be sufficient), then you can compare the mean between the two groups as long as the data appears to be normally distributed.

2) If the distribution is skewed, then you can resort to non-parameteric test as Carlo suggested.

The label of the variable shouldn't be a problem is you want to compare the mean or median.

Hi Mohammed,

I am not a SPSS user either, I'm more familiar with Stata, R, and SAS. But I'm not sure why you're worried about coding Gram+ and Gram- with 1 and 2. The way I understood your experiments, your dataset would looks something like this:

              #Gram+       #Gram-

egg1        25                    30

egg2         3                     23

.............................................

eggn        34                    55

So, in this situation and for your research question, naming your variable Gram+ "1" and your Gram- "2" does not affect the math of your mean/median comparison. 

As Carlo and Prabin said, if you have a large n (and this is a debated number), then you can assume your data is normally distributed. I usually run normality plots (http://www.stattutorials.com/SPSS/TUTORIAL-SPSS-Assess-Normality.htm) and normality tests(http://www.maths-statistics-tutor.com/normality_test_pasw_spss.php) to make sure. 

Normality tests and plots will rarely give you a black or white answer, so you'll need to make a decision based on the amount of evidence for or against normality. 

If the variables (Gram+ and Gram-) are normally distributed, then you can use the t test to compare means. 

If the variables are not normally distributed, then use a non-parametric test (which compares medians, rather than means), like the Mann-Whitney test or any of the other suggested ones. I will run them all to see if the results differ in terms of statistical significance. However, for write-up purposes, you need to stick to one test and justify its use.

I'm not familiar with the maximum-accuracy methods that Paul suggested, but they sound very attractive. I don't know if they are already implemented in statistical programs.

Thanks for your answers all, here is a pie charts shows frequency of Gram+ve and -ve bacteria, would it better to show if there is a significant difference or the chart is enough to conclude that? 

Mohammed,

If the abundances of Gram+ve and Gram-ve bacteria were measured from different eggs, then the Gram+ve and Gram-ve data are independent of each other.   In this case, a non-parametric test to compare the median abundances across the 2 groups is, as Carlo mentioned, the Kruskal-Wallis test.   In microbiology, it is very common to log10 transform the abundances.   One reason for this is that abundances tend to span many orders of magnitue.  A second reason is that the variance tends to increase with the mean.  The third reason is that log10-transformed abundances tend to be normally distributed.   So another option, that I personally prefer, is to apply a Welch 2-sample t-test (i.e., do not presume equal variances across the 2 groups) to the log10-transformed abundances.  This will help you answer whether there are differences in the mean log10 abundances (which is equivalent to testing whether the median abundances are different when the log10-abundances are normal).

If the abundances of Gram+ve and Gram-ve bacteria were measured from the same eggs, then the Gram+ve and Gram-ve data are dependent.   My opinion, in order to deal with the dependence in this case, is to apply a matched pairs t-test to the log10 abundances.

From your picture, it appears that you really may be interested in comparing frequencies of eggs that have either  Gram+ve and Gram-ve, in which case you would use a different test entirely (a test of proportions or a chi-square test).

Many thanks to you all 

Mohammed, as I understand it, categorical variables are nominal in nature and can only be measured in terms of counts (frequencies) and percentages. They are not cardinal (ratio, interval) and hence cannot be measured in terms of "means". They do not have "mean differences" to test.

The way you data is presented leads to think about a test of proportions of Gram+ (or Gram-) in different populations. If the number of bacteria tested in large enough, you may use the normal approximation of the binomial?

Hello Mohammed, You have input the data in the standard way for SPSS to handle. The test to do depends on your hypothesis. You might be interested in the ratio of gram+ to gram- bacteria. I would  make 95% confidence intervals for the proportions and compare them. However, the numbers of bacteria in our food are important for food safety, so you may be able to apply a parametric test.