A t-test for percentage data is ok if the sample size is decent (n>20, say) and/or the values are not very close to 0.0 or 1.0. If this is not the case, you may consider ato trasform the data before you test it. The logit-transformation would be appropriate for percentages.

The p-value is a "surprise index" of your observed data whe assuming the null hypothesis. The closer this value to zero, the more "surprising" or unexpected is data like yours - under the assumption of the null hypothesis. If it is "quite surprising", you would reject the null. Usually, "quite surprising" imeans p < 0.05. If your data is less surprising, one would not take this as a reason to reject the null. Your p-value is 0.24, what is not at all surprising. By all conventional standards this is not enough to reject the null hypothesis. The "conclusion" is that your data is not conclusive regarding the null hypothesis. There is not enough information in your data to interpret the sign of the estimated mean difference.

To your second question: yes.

Joe Kristoffer Partyka . Your null hypothesis would say that the rural and developed area have "equal" means. As Jochen Wilhelm says, you shouldn't reject that hypothesis unless you have a very "surprising" p value (

It seems to me that a Chi-square test or Fischer-Exact test would be appropriate instead. The first variable is categorical, i.e. presence of infected blood cells (Yes/No) and the second variable would again be categorical like place of residence(rural/urban), SES (high/moderate/low) and so on. So, you would be actually testing whether a particular attribute (e.g. place of residence) is associated(not correlated) with having infected blood cells. In other words, you will be testing whether the proportion of infected blood cells is different between two groups (e.g. rural vs urban). If P-values is significant, you conclude that proportion of people with infected blood cells is different in urban and rural people, in other words place of residence is associated with having infected blood cells.

We need to clearly identify which is a categorical variable and which is continuous before we start. Similarly, correlation is not same as association. Correlation is just one of the ways we can assess association.

I have summarized tests of association:

Categorical vs categorical variables: Chi-square test (if number of cells with expected frequency less than 5 is less than 20% of total cells), else Fischer Exact Test

Categorical(2 categories) vs continuous variables (for independent samples): Compare mean using Student t-test (Independent sample t-test) with equal or unequal variance depending on variances of the two groups if continuous variable is in normal distribution, Compare median using Mann-Whitney test (Wilcoxon rank sum test) if continuous variable is in non-normal distribution

Categorical (2 categories) vs continuous variables (for dependent samples): Compare means using Paired t-test if normal distribution, Compare median using Wilcoxon sign rank test if non-normal distribution

Categorical (>2 categories) vs continuous variables: Compare means using one-way ANOVA if continuous variable is in normal distribution and variances are equal, else compare medians using Kruskal Walis test

Continuous vs continuous: Pearson Correlation test if both continuous variables are in normal distribution, otherwise Spearmann correlation test

If your sample size is small (n

I see I made a huge booboo there in stating that I should have discarded my null hypothesis, thanks for clearing that up for me and for helping me with my statistics.

Much appreciated

Dear Joe Kristoffer Partyka , I agree with John-Kåre Vederhus , your null hypothesis with this p value is acepted. In addition Laura Ellyson test suggestion of non-parametric test could help you to compare these two independent samples.

There are several material that help you to choose your statistical tests. This book could be useful for you:

"Choosing and Using Statistics: A Biologist’s Guide" wrote by Calvin Dytham.

Best,

Cristian

Dear Cristian, sorry for bein nit-picky, but there is nothing like "accepting the null hypothesis". The test is done to see if the data at hand is sufficient to reject it. If this is not the case, get more data or live with the fact that your data is not (sufficiently) conclusive regarding the null hypothesis. The fact that a p-value is large is no indication whatsoever that the null hypothesis is reasonable, probable, or true. The way you phrased it leads to the error of taking the "absence of evidence (for an effect)" as "evidence of absence (of an effect)".

Jochen Wilhelm you are correct, I use the incorrect words. Thanks for your observation.

In this case and with those data there are no differences between both samples. The correct sentence should be "there is not enough evidence to reject the null hypothesis". As Jochen Wilhelm said.

In the case that our sample size is larger (enough to make a more robust conclusion) we could say that if there are equality of means, am I correct? Or would the lack of evidence to reject the null be assumed in both cases?

Regards,

Cristian

Dear Laura and Christian, In addition to what Jochen Wilhelm says, rank-based tests are only tangentially related to the median. In many cases, it is not clear that they are valid tests of hypotheses about medians. Jochen has explained this clearly on other occasions. This does not mean that you can not use them to study the relationships you want, but that the interpretations of the results are different and it is better not to do them in terms of the medians.

A rejection test can in principle (logically) not measure "evidence for equality". If you have more data, you are more likely able to reject the null for smaller differnces in the sample means. One can calculate the probability (aka "power") to reject the null for a given population difference; let's call this difference D. In Neyman/Pearson A/B tests, D is specified and the required sample size is calculated to achieve the desired power. If the power was chosen reasonably large and the data is not significant, then it is reasonable to believe that the population difference is smaller than D. The smaller you choose D, the larger will be the sample size to get the desired power. If you chose D=0, you would need an infinitively large sample size. So there is no way to show that D=0.

If D and the the sample size is not pre-specified, one can have a look at the confidence interval. The outer limits can be seen as "likely" upper bound for D, which is supported by the data. This is some "half-way Bayesian" interpretation. Using "two one-sided t-tests" (TOST) is a similar, logically equivalent approach.

Even better is a proper Bayesian approach. Specify a reasonable prior, let it be modified by the data, and interpret the posterior. The outer bounds of the credible interval serve as upper "credible" bound for D.

use non parametric tests like Chisquare/Fishers exact test, If outcome measures are on scale use tests like t test or mann whitney U test, All depends on what type of outcome measures you try to analyse.