Comparing Compression strength of chocolates

[Stevo6754]

Hey there, I am currently working on a project to compare the compression strength of chocolates with different inside filling (caramel, nuts, coconut). I came up with the hypothesis that chocolates filled with nuts would require the most force to break while chocolates with coconut the least, caramel being in the middle.

I constructed a device in which I could measure the amount of force required to break the chocolates and took 30 samples from each chocolate.

I calculated the sample mean and sample standard deviation for each chocolate.

My problem is is that enough to come to a conclusion regarding which is strongest?

I looked into doing a normal standard distribution since this is continuous, but the more I thought about it the more confused I got. For one I don't know either the population mean or population standard deviation. Population mean isn't an issue since I can assume it to be the sample mean for n>=30 (which is the case). But when I look at examples for standard normal distributions they aren't similar to my experiment in that they usually have a hypothesis with a fixed numerical value and are trying to refute the claim.

I have 3 different chocolates here, no numerical values in my hypothesis. I'm sorry if this doesn't make sense but the more I'm reading the more confused I'm getting. I'm looking into regression analysis at the moment but I still don't know how that would relate the 3 different chocolates.

Any direction/help would be greatly appreciated, thanks!

 

[jim mcnamara]

I assume you want to establish if the results for the samples are from different populations, or are from the same population. You worked out a standard deviation for each group of chocolates. I assume you controlled other variables, like temperature of the samples, chocolate tempering, % cocoa solids, wax content, etc.

Your first step is to look at the data and the standard deviations. If the means all fall within +/- 1 standard deviation of each other then you probably have found no difference.

I am guessing you want a method. If the populations appear "separated" it is worth trying an analysis. Have a look at a one-way ANOVA for starters - this page does the work for you:

http://www.danielsoper.com/statcalc3/calc.aspx?id=43

This assumes that you used precisely the same chocolate (what you are testing) with the same thickness etc.

 

[chiro]

Hey Stevo6754.

I would not default to normal distributions for testing data and doing statistical analyses on them just because Normality is easy to work with.

The best advice I can give (given your information) is to establish distributions either based on empirical data (so the data you get when you try and crush a chocolate of some type) or based on a model derived from assumptions.

In terms of just making a comparison of what nuts are the most susceptible to breaking or being crushed, I recommend considering looking at proportions for each type with a proportion of breaking for each class of chocolate type.

You can then do a test of proportions and compare first if there is any statistical difference between any of the proportions, and later do a test to see what the statistically significantly pairs of proportions are.

So this is to test the amount of breakages.

With regards to the compression strength, I might suggest that you consider choosing bin sizes for various forces and then model a distribution for each of these forces to see how many attempts break the chocolate and how many don't.

You can then take these bins and do a test for where a statistical "break point" happens with regard to the force for breaking (so after the critical point, all chocolates statistically significantly break but before they don't).

I make the above recommendation because of the nature of how stress works in materials and how the internal force characteristics of materials make it hard to actually assess stress characteristics based some kind of continuous variable.

Its like when you take a plastic object with various properties and you bend it until one point the whole thing snaps and this point is the critical point.

Assessing what this critical point is (in the context of your chocolate experiment) and taking into account the nature of stress and strain for the material itself is going to give you not only more reliable analysis, but a more reliable interpretation.

I don't know a lot of deep knowledge about stress and strain properties of materials (but I do understand the basics from prior coursework) and what I do know is that understanding these critical points, the assumptions for the material properties (elasticity, etc) and then taking all of this and formulating very specific models, test-statistics, and critical values will give you something that not only makes sense both physically and statistically, but also allows you to extend such things if you want to go deeper and make further inferences.

This actually sounds very involved but I think that at the least, you can do a test of proportions with an ANOVA for the proportions to see how they rank in likelihood of breaking.

 

[Stephen Tashi]

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I have 3 different chocolates here, no numerical values in my hypothesis!

To apply the statistical method called "hypothesis testing", the hypothesis must be specific enough to imply something quantitative. The usual type of hypothesis testing assumes something along the lines of "there is no difference" and tests whether some aspect of the data has a high or low probability based on that hypothesis. (Such a test does not quantify the probability of the hypothesis being true and it does not quanify the probability of the hypothesis being false. It only quantifies the probability of the data assuming the hypothesis is true.)

If you can't quantify the probability of some aspect of the data by using your hypothesis, your hypothesis is too vague to use in hypothesis testing.

Besides hypothesis testing, another use of statistics is in estimation. Perhaps estimation is what you should do. (You didn't explain why you are doing this. Is it a science project?)