# Which statistical test for statistical significance of positive result in 5 categories of samples

I have 5 categories rock samples and I am trying to understand how their fossil preservation differs and whether the difference is statistically significant. I determined the presence or absence of fossils using a spectroscopy tool in rocks representing 5 sample categories. I obtained the percentage of positive occurrences. I then repeated the measurement 10 times in each category and obtained a mean percentage for each category.

• What test do I use to understand (1) if and (2) how the means of the 5 categories are statistically different from each other?
• Can I then rank the categories in their preservation potential to contain fossils?
• Is repeating the test 10 times per category enough?
• Do I understand correctly that you have 10 yes/no measurements from each of 5 different types of rocks, & you want to know if the proportion yes differs? Re how much data you need, that is a question about power-analysis; you don't have enough information here to answer it, but if you click the link you can read our threads on the topic. – gung - Reinstate Monica Mar 28 '15 at 2:28
• Gung, I have 5 categories of samples and 10 is an arbitrary number of measurements I was going to make on each to determine a yes/no presence of a phenomenon. Yes, I want to know if the categories have a statistically significant difference in "yesses" or presence of that phenomenon. – Anonymous1717 Mar 29 '15 at 5:46

Your data are appropriate for a chi-squared test. You can form a contingency table by entering the counts of each type that did and did not have fossils in them. For example:

            marble  quartz  granite  sandstone  mica
w/ fossils       5       1        6          8     1
no fossils       5       9        4          2     9


N.B., if those were your numbers, the results would be:

        Pearson's Chi-squared test

data:  as.table(x)
X-squared = 15.9278, df = 4, p-value = 0.003118