Determining Sample Size - Filling a bag with three different types of candy

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PerfettiFUN

#11
Yes - there are set formulas for both the theoretical distribution of colors and what sample size you will need.
so you know what they are or where i could find them? even if it is unrealistic to take that number of samples i would like to know what the number is.

oh, i was also wondering if i should be using a chi-square to tell whether the current state and a random sampling of candy going into the bag are statistically similar. i think when doing a minitab it gives you sample size for a chi-square but i don't have it on my computer to mess around with :(

BTW thanks again for all the help and suggestions, i am just a co-op right now so i haven't designed many experiments on my own before so just trying to make sure i am doing things the right way before i go to present it to my boss :D
 
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M

M Komarmy - 2012

#12
I would use a two sample T-test to compare the 2 sample means of each color before and after your process change . The Chi-square is better for attribute or count data.
 
P

PerfettiFUN

#13
I would use a two sample T-test to compare the 2 sample means of each color before and after your process change . The Chi-square is better for attribute or count data.
that is why i was going to use chi-square, since the number of bars of a certain color in a bag is a count doesn't that make it attribute data? or am i wrong in thinking that this would still be considered attribute instead of continuous?
 
M

M Komarmy - 2012

#14
I guess my line of thinking was to record the number of each color in 30 to 50 bags (each color could theoretically be anywhere from 0 to 30 pieces). So you would have 30-50 data points for each color (three columns of data) for the current process, and three columns of data for the changed process. Even though the data is not continuous, you can still look at the mean and variance in each column and see if the process change has improved the output. Compare in minitab the before and after columns for each color.

If there is a bias in your process that prevents the mixture from being random, the before data will show that some of the colors are different than the others or from the target (assuming you want them each to be equal at 10 per bag). If your process change is effective, you will show a mean value for all colors that is nearer to 10.
 
P

PerfettiFUN

#15
oh okay, i got what you're saying. that is how i envisioned taking down the data too, unfortunately we are shut down today doing some 5S cleaning so it isn't running today. so next monday hopefully i will be able to start collecting some data.
 

Stijloor

Staff member
Super Moderator
#16
oh okay, i got what you're saying. that is how i envisioned taking down the data too, unfortunately we are shut down today doing some 5S cleaning so it isn't running today. so next monday hopefully i will be able to start collecting some data.
:topic:

Just curious; do you have a shift key on your keyboard? :D

Stijloor.
 

Miner

Forum Moderator
Staff member
Admin
#20
that is why i was going to use chi-square, since the number of bars of a certain color in a bag is a count doesn't that make it attribute data? or am i wrong in thinking that this would still be considered attribute instead of continuous?
You need to consider the hypothesis that you want to test in addition to the type of data.

With count data, you have two options. The first is to treat it as count data and use a test for discrete data. But there is a second option. You can use the Freman-Tukey variance stabilizing transform for count data, and analyze the transformed data as variable data.

In your situation, there is also a third option. You are dealing with a mixture, so you can also treat the data as a proportion.

While you are correct that Chi-square is suited for count data, the hypothesis tested may not suit your needs. For the Chi-square Goodness of Fit test, the null hypothesis is an expected count of 10:10:10. If Chi-square is significant, you reject the null hypothesis and conclude that the counts do not equal 10:10:10. This will confirm that you have a problem, but no more.

You can perform a 1-sample t-test with the transformed data to test whether the count is significantly different from 10, or do a proportions test on the proportion data. This can provide directionality to the problem, but little more.

I recommend performing a Poisson capability study. This is typically used for defects (which are count data), but can be interpreted as you need. It will provide the percentage of a given color with the expected variation about that percentage.
 
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