Strange question?

[kramtronix]

I have been handed a task that my brain cannot quite wrap itself around. Skipping the details and getting down to brass tacks, I am basically looking for ideas on how to measure CONSISTENCY.

As an example, if a factory manufactured watches in the following fashion, how would I measure the CONSISTENCY in which the factory does so?

[Factory is open 8 hours a day]

Hour 1: 240 watches
Hour 2: 245 watches
Hour 3: 375 watches
Hour 4: 520 watches
Hour 5: 300 watches
Hour 6: 750 watches
Hour 7: 200 watches
Hours 8 200 watches

Obviously, the variance of watches per hour need to be compared to each other, right? However, after that is where I get lost. Any pointers or tips would be of great help!

 

[SydneyGeek]

Typically, you'd use some of the inbuilt stat functions in Excel.

AVERAGE -- To get the mean # of watches / hour
MEDIAN -- To get the midpoint of the distribution
STDEV (or STDEVP) -- Standard Deviation measures the spread of a bunch of figures. Basically, these are used to determine the spread of a normal distribution.

1. If the median and mean are very different your data is skewed
2. If the STDEV (SD) is high you have a large amount of scatter. Low STDEV indicates a tight distribution. Generally, 95% of values in a normal distribution fit within 2 SD of the mean.

Denis

 

[kramtronix]

Disregarding the watches example, I ran those formulas on the data I'm trying to measure the consistency of. Here's what I came up with:

AVG 68
MEDIAN 72
STD DEV 25

The SD of 25 seems low, and is way off compared to the AVG and MEDIAN.

 

[Richard Schollar]

The Standard Deviation is measuring something different to the two average values you quoted (Mean and Median) - as Denis pointed out, it is measuring the spread of the values ie given a dataset of:

Hour1: 250 watches
Hour2: 250 watches
Hour3: 250 watches
Hour4: 250 watches

you'd have a Median and a Mean of 250 but a Standard Deviation of 0 (as there is absolutely no variation in the numbers of outputted watches).

Your SD of 25 just gives you an idea of how variable your data points are about the Mean (average).

 

[SydneyGeek]

Thanks Richard

I should have clarified my suggestion before, but your explanation is spot on.

Kram, to give you an idea of what lies behind the standard deviation, take a look here:
http://www.24hgold.com/printarticle.aspx?pagedest=227403&langue=en&viewarticle=True

http://www.soe.ucsc.edu/classes/ams005/Winter05/class3.4.pdf

The second is more technical but both should help

Denis
http://www.soe.ucsc.edu/classes/ams005/Winter05/class3.4.pdf

 

[kramtronix]

OK - I get it now. I guess I just didn't understand the real concept behind standard deviation. I'm new to statistics. Thanks!

Now, I have another question.

I am trying to see the effects of a new process. I'm going to gather the standard deviation of each day's intervals for 3 months prior to and after the new process. (Our days have 22 intervals) Then, I'm going to run an average on the STDEV from the months and compare them to each other. Would this be junk metrics? It's not like an average of an average or anything, but I want some feedback on the theory.

 

[Richard Schollar]

I think you'd want to use some kind of weighted average based on the total outputs for each period - otherwise you will run the risk of skewed rsults. However, I'm no mathematician so...

 

[kramtronix]

Well, the numbers I'm running the STDEV on are in fact weighted. Does that help my case? LOL

So I have this weighted percentage that I'm trying to measure the consistency of. And what I want to see is, the amount of deviation, or "scatter" as mentioned about, and compare it to the amount of deviation AFTER the process.

Does that make sense?

 

[Oaktree]

You might read up on (either in Excel help or by Googling it) ANOVA (ANalysis Of VAriance).

Your test is a perfect use for ANOVA analysis.