Help to compare data - 3 groups (15 batches each) collected over 3 consecutive weeks

Z

zecarlin

Hi all!

I have one doubt how to compare 3 groups of data from the same source. I'll explain below:

* I collected the rework time from 15 batches on week 1;
* I collected the rework time from another 15 batches on week 2;
* I collected the rework time from another 15 batches on week 3.

The time decreased during the collection from week 1 to week 3.

When I made a Probability plot on Minitab 16, in 2 cases I had non-normal distribution, so, I can't use the mean of 3 cases to compare.

What can I do? How can I compare this 3 groups? I wanna prove the time reduction!

Best regards.
 
B

Barbara B

Re: Help to compare data

First I would recommend to take a look at the data, e.g. with grouped boxplots. There could be a time reduction over the three weeks and/or a reduction in variation.

Since the test for normality was made and a (significant?) deviation for two out of three groups/weeks was found, there could be other factors present in the process. If the process outcome (rework time) does come frome the same source, the behaviour of the data should be similar, but you altered something in the process to reduce rework time. Therefore I would be extremely cautious with the "same source" assumption.

An alternative to a comparison of means (for more thant 2 groups this could be done via ANOVA) could be a nonparametric test like the Kruskal-Wallis test for differences in medians:
Stat > Nonparametrics > Kruskal-Wallis
Response: rework time
Factor: week

The Kruskal-Wallis test requires continuous data within the groups, but not necessarily normally distributed data.

It would be helpful to elaborate more specific ideas to take a look at the data itself. Could you please provide the data set?

Regards,

Barbara
 
A

Allattar

Re: Help to compare data

What do the normality tests look like. For a single page combine them on the layout tool. Or use the Probability plots from the Graph menu. Select Single, and then use multiple graphs and the by variables tab to split them by group.

We can probably get an idea about the data and what we are seeing from the probability plot.
 

Bev D

Heretical Statistician
Leader
Super Moderator
Re: Help to compare data - 3 groups (15 batches each) collected over 3 consecutive we

If you post your data we can probably provide an effective answer or two.
 

Statistical Steven

Statistician
Leader
Super Moderator
Re: Help to compare data - 3 groups (15 batches each) collected over 3 consecutive we

Typically I start with ANOVA analysis (one-way) with week as the single factor. I look at the residuals for each of the three groups. If there is a pattern showing a lack of homoscedasticity, I use a Wilcoxon non-parametric test.
 

Bev D

Heretical Statistician
Leader
Super Moderator
Re: Help to compare data - 3 groups (15 batches each) collected over 3 consecutive we

I use the Tukey-Duckworth tests or my flux capacitor when all else fails. ;)

Seriously tho, what you are hearing is that the appropriate statistical analysis cannot be selected without seeing the data. Additionally time is typically skewed and therefore naturally not Normal. This makes the selection of the appropriate analysis even more complex since there is rarely a 'typical' answer. That's why posting your data is critical to getting a useful answer.
 
K

KLDLetts - 2012

Re: Help to compare data - 3 groups (15 batches each) collected over 3 consecutive we

I would probably argue that your sample is not large enough to determine if it is normally distributed. (Although I am commenting without seeing the data).
 
M

mandarkg

Re: Help to compare data - 3 groups (15 batches each) collected over 3 consecutive we

I suggest using ImR (Individuals & Moving Range) control chart. Calculate the control limits for each week. Then see if the means and variances change with each week. This can be done along with Kruskal- Wallis test suggested by Barbara.
 
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