Measure the mass distribution and plot percent less than on lognormal probability graph. Check wikipedia and references therein.

What is your purpose? Are you trying to see if the size distribution changes after milling? Or if there are differences between the powders?

1-way ANOVA is used to compare one variable (say size) between 3 or more groups to tell you if they are different or same -for instance if the size distribution  is significantly different between the 4 groups.

A 2 way ANOVA allows you to determine the effect of 2 factors -for instance what is the effect of milling on the 4 drugs. Milling would be one factor, drug the other. ANOVA would answer the questions: is the response affected by milling? By drug type? Do the two factors interact? You'd need to look for a statistics software to run 2-way ANOVA.

@Debora berti

Thank you for your time,

1)Fpr my first experiment I am trying to see if the particle size distribution changes after milling

2) 2nd experiment is to show if the particle size before and after milling affects flowablity at different speeds using an avalanche tester

Hi Aslyah,

I'm going to try to give you an answer but since you know your field and data the best, you may also want to look up t-test and ANOVA (1-way and 2-way) analysis yourself to get better understanding about what they can tell you, how to use them and what assumptions they make. A few resources on the web:

https://statistics.laerd.com/spss-tutorials/one-way-anova-using-spss-statistics.php

http://statistics-help-for-students.com/

http://www.real-statistics.com/two-way-anova/two-factor-anova-without-replication/

https://www.gnu.org/software/pspp/

First of all, you say you took 3 measurements each time; some statistical programs let you enter replicates, others do not -in the second case I would use the mean of the 3.

Also, I would first plot the data and look at the general distribution (excel can do distribution), are the size distributions approximately normal? Are they skewed or binomial? It is easier to analyze normal distribution, and often you can transform the data to make the distribution normal, for instance you can do the log of grain size.

From your answer, I understand that you are not interested in differences between the 4 drugs but they are just 4 different samples.

Now for question 1:

In this case you have 2 groups: before milling and after milling and 4 samples, and you measured grain size distribution for each. If the distributions are normal, the mean grain size is a good variable to represent their distribution. You took repeated measures of the 4 samples, so your data are paired. Anova is commonly used for 3 or more groups, the t-test is the correspondent for 2 groups, like in this example.The t-test will test the hypothesis that there is no difference in mean grain size between the 2 groups (before and after milling) –this is the null hypothesis. If the resulting p is less than 0.05 (5% confidence level) then you can reject the null hypothesis and say that milling has a significant effect on mean grain size. Note that you are basing your decision on only 4 samples though.

Question 2:

For this question you can use a 2 -way ANOVA. I'm going to make an example that hopefully helps you get started. It is certainly not the only way to set it up or the only option just a help to move forward.

Say you decided you can make 2 groups with grain size: before milling and after milling.

I never used an avalanche tester, I'm guessing you set the speed before running your test, so say you repeat your test at 3 different speed levels.

So far you have factors 1) grain size with 2 groups and factor 2) speed with 3 groups. You can create a table that has the speed levels as columns (column 1: low speed, column 2: medium speed, column 3: fast speed) and grain size groups as row (row 1: before milling, row 2: after milling), each cell of the table corresponds to a combination of the 2 factors (before milling-low speed, after milling-medium speed etc.) that you need to collect flowability data for.  Note that if you use 4 drug samples and for all combinations these are repeated measurements. You need to specify in the statistics program that you are doing repeated or paired measures.

The two-way ANOVA test will then test 3 null hypotheses: 1) Grain size does not affect flowability 2) Speed does not affect flowability? 3) Grain size and speed do not interact.

Hope this helps,

Debora

@debora Thank you so much for your feedback its definitely cleared a few things up!Much appreciated .