topic Re: Creating a Sampling Distribution in Discussions

Creating a Sampling Distribution

tmfortney — Tue, 23 Apr 2019 16:38:57 GMT

I would like to create a true sampling distribution from my dataset and I am not sure what formula(s) to use in JMP to create it. I have a population dataset of 10,000 and would like to create a sampling distribution with n=100, which would then result in 100 sample means. What formula do I use to create this in JMP?

Re: Creating a Sampling Distribution

Mark_Bailey — Tue, 23 Apr 2019 17:03:46 GMT

First of all, a sampling distribution of what? We usually think of a sampling distribution with respect to an estimate, like the sample average or a slope. Is kind of thing what you are after? If so, what estimate?

Second, the sampling distribution assumes sampling with replacement. That operation would be difficult using column formulae.

Third, it usually takes many draws to get a good sense of the sampling distribution. Again, this iteration would be difficult using column formulae.

Fourth, do you have JMP Pro? There is a built-in bootstrapping feature that will re-sample your data to obtain new estimates of the statistic. I can't remember if you can specify the size of the draw or if it always uses the original sample size.

I think that a script might be necessary.

Re: Creating a Sampling Distribution

tmfortney — Tue, 23 Apr 2019 17:11:17 GMT

Thanks for the response. So, I have population data from my call center regarding the length of phone calls over the course of a month and the data is not normally distributed. My thought was to perform random sampling of n=100 per sample, which would help create a normal distribution. I know there are other ways to do this but I wanted to understand how to do this in JMP. I do not have JMP Pro so this may not be possible based on your text below. Does this make more sense what I am asking?

Re: Creating a Sampling Distribution

Mark_Bailey — Tue, 23 Apr 2019 17:18:56 GMT

I just read your original post again. You want to compute a sample mean of Y, whatever that data happens to be? Just calculate it. The sample average is still the unbiased estimator for the population mean.

How will the sampling distribution help you? What would you do with all the estimates from many sub-samples of N = 100?

Also, what are you trying to do such that a normal distribution is assumed?

Re: Creating a Sampling Distribution

tmfortney — Tue, 23 Apr 2019 17:29:53 GMT

Well, I guess I need to give some additional background on this. Where I am going with this is I would like to do is look at the different call center agents and perform an ANOVA test to determine if there are statistically significant differences in the average length of call time between agents. However, when you look at the length of call data for each agent, the datasets are not normally distributed and I am violating homogenity of variance when I compare the sets. Based on the central limits theorem, if I peformed a sampling distribution for the 10,000 (approximate) calls each agent performed that month with n=100 it should then be more normally distributed. I also considered using a Welch's t-test for unequal variances, but I was not sure if this would fully address the issue. I know there are other ways to normalize the data, but I also thought it would be useful to know how to perform sampling distributions in general using JMP. I may be going about this the wrong way so any additional advice would be great!

Re: Creating a Sampling Distribution

txnelson — Tue, 23 Apr 2019 18:34:58 GMT

Here is one way to create the sample means. If you saved and concatenated the tables, rather than deleting them, you could actually use the samples to do analyses on.

Names Default To Here( 1 );
dt = Open( "$SAMPLE_DATA/semiconductor capability.jmp" );

dtMeans = New Table( "Final", New Column( "Sample" ), New Column( "NPN1 Mean" ) );
dtMeans << add rows( 100 );

For( i = 1, i <= 100, i++,
	dt2 = dt << Subset( invisible, Sample Size( 100 ), columns( :NPN1 ) );

	dtMeans:Sample[i] = i;
	dtMeans:NPN1 Mean[i] = Col Mean( dt2:npn1 );

	Close( dt2, nosave );

);

Re: Creating a Sampling Distribution

Mark_Bailey — Tue, 23 Apr 2019 19:06:23 GMT

Now I understand. The ANOVA assumes that the random errors are normally distributed. So let's not use ANOVA!

There is a simple way around all of your issues. First of all, the length of call time is generally not normally distributed. It is a measure of the life of the call or simply life time data. More generally, it is time to event data (event is end of call). You want to use Analyze > Reliability and Survival > Life Distribution instead of ANOVA. Select the Compare Groups tab at the top of the launch dialog. Select the column with the length of the call values and click Y, Time to Event. Select the column with the values that identify the agents and click Grouping. (Big assumption for now but let's get things going: all the calls were completed. That is, none of the length of call observations represent incomplete calls. That situation is known as censoring. We can deal with that case properly later if necessary.) Now click Go.

I suggest using the Weibull distribution model and scaling. Click the checkbox before Weibull and the radio button after Weibull. You are going to get a lot of information back at you.

First, the plot at the top in Compare Distributions is useful to visually assess goodness of fit and assess differences between agents. Second, the Summary report informs you about each agent. Open and examine the Wilcoxon Group Homogeneity Test. It assumes that the distribution of all the agents is the same but is significant if any agents are different. Third, there is a tab with an analysis of each agent. Each report is detailed and specific. You might not need or want all the information.

I will stop here and see if we are going in a good direction and if you have further questions.

Re: Creating a Sampling Distribution

P_Bartell — Wed, 24 Apr 2019 13:32:29 GMT

Too add a bit to @Mark_Bailey 's recommended solution, I'll throw in another issue. What about focusing on the mean (or have you thought about median instead?) AND the variance/spread? Recall Jack Welch's famous quote, paraphrasing, "Customers rarely experience the mean...they feel and experience the variance." So if your ultimate goal is to improve or make more consistent AVERAGE contact length...I encourage you to also think about minimizing/reducing variance when your ultimate goal is improved customer satisfaction through reducing contact length VARIANCE.

Re: Creating a Sampling Distribution

tmfortney — Wed, 24 Apr 2019 14:06:21 GMT

Thanks for the advice and instructions. I have never used this platform but after reading more about it I see how it could be very useful in this situation. However, I am having some difficulty reading the output. I see under the Wilcoxon Group Homogeneity Test that the p-value is <.0001 so the variances are definitely not homogenous. With ANOVA I usually look at pairwise comparisons and can compare, but I am struggling with how to compare the Weibull. As you mentioned, I can visually assess the goodness of fit under Compare Distributions, but is there a way I can statistically determine the difference (like p-value) as we do with ANOVA?

Re: Creating a Sampling Distribution

tmfortney — Wed, 24 Apr 2019 14:08:49 GMT

Very true and a good comment. I usually make it a point to look at both the medians and the spread of the data to determine if the process is in control. Thanks for the feedback.

Re: Creating a Sampling Distribution

Mark_Bailey — Wed, 24 Apr 2019 14:18:50 GMT

You are correct, there is no analog to the choices for multiple comparisons as found in the Oneway platform.

The Wilcoxon test is an omnibus indicator of any difference. It is not specific to one parameter like the mean or variance. The plot at the top can help there, though. Parallel lines have the same variance or scale. Displaced lines have different mean or location. So if one agent is consistently completing their calls more quickly, their curve would shift to the left.

You also have the parameter point estimates and confidence intervals for each group (agent) for comparison, although that information is not the same as a multiple comparison test.

You can also use the profilers to extract information about each group. These answers are provided both as a point estimate and interval estimate.

I am not apologizing but simply recognizing that the methodology here comes from the reliability engineering field. The same methods were independently discovered in medical mortality and morbidity. The terminology, therefore, pertains to those fields but the methods are none the less relevant. It just requires a bit of translation. Sometimes it also requires reversing the goals. In reliability, an increasing hazard function is bad. In your case, though, it is good. It means that an event is more likely to happen. But in your case an event is not a failure, it is a completed call.

There are analogous methods for regression models with time to event data. So if you had covariates, you could include them in the model for lifetime and test them. There is a lot of flexibility here.

Re: Creating a Sampling Distribution

Mark_Bailey — Wed, 24 Apr 2019 14:20:35 GMT

You can use the profilers in Life Distribution to get more than the mean or median. You can estimate any quantile (time) or probability you like.

Re: Creating a Sampling Distribution

tmfortney — Wed, 24 Apr 2019 14:25:06 GMT

Thanks- this helps a alot. It definitely helps me with what I am trying to do. One last question- if the variances were equal and the population were normally distributed (or my sample size was sufficiently large) I could have used an ANOVA as I have in the past, correct? I just want to make sure I am not using the wrong tool for the job.

Re: Creating a Sampling Distribution

Mark_Bailey — Wed, 24 Apr 2019 14:45:55 GMT

Yes.

If the variances were unequal but the errors were normally distributed, then you could use the Welch ANOVA, which JMP automatically provides if you select Unequal Variances from the Oneway platform menu (red triangle).

Life Distribution is the right tool in this case, as far as I can tell.

Re: Creating a Sampling Distribution

P_Bartell — Thu, 25 Apr 2019 15:03:32 GMT

Then if you want to really go crazy, if you have access to written transcriptions of calls (say in a .txt file) AND JMP Pro...then a whole world of Text Analytics and Predictive/Exploratory modeling work is at your fingertips. With JMP Pro you can analyze the free form text of agents conversations using simple word/phrase counts up to and including latent class analysis, topic analysis, and latent semantic analysis for exploration. From there between the document term matrix or other dimensionality reduction methods, it's a short leap over to the Generalized Regression platform and the quantile regression capabilities for modeling text (or it's surrogates) to contact time quantiles for median or say, 95th quantile. Now you have a link between words and talk time! And if you have customer satisfaction scores wrt to an engagement you can model these as well. Here's a link to a Mastering JMP event that illustrates much of this workflow:

https://www.jmp.com/en_us/events/ondemand/mastering-jmp/using_text_explorer_to_extend_analysis.html

Re: Creating a Sampling Distribution

nil — Mon, 13 Jan 2020 13:40:34 GMT

Hi txnelson, Thanks for script on sample means. I am new to JSL and need your help to correct the script which I had tried on my data. Data table and script attached for reference. I just followed (based on limited understanding) the script you have posted. However, the final table observed was blank. Please suggest..
I would need Final table with 100 sample mean, each of 3 samples, from original data table.

Data Table (Table Name: BPN) Contains BPN content value (in %) from 60 individual units/ vials.
BPN
103.2
100.3
99.2
103.6
102.1
100.6
100.1
99.6
99
102.6
101.2
97.6
102.1
100
102.4
101.7
105.3
103.7
99.1
103.1
99.3
99.2
98.5
101.7
106.3
97.8
104.6
102.9
103.1
101.8
101.8
99.9
102
100.6
106.6
100.6
104.7
98.4
95.6
103.2
103.5
101
102.8
100.5
97
104
99.8
103
103.4
101.6
100.6
101.9
101.2
99.7
101.1
101.1
99.2
104.9
103.4
106.4

Script: (with data table open, I tried with script below)

dtMeans = New Table( "BPN Mean", New Column( "Sample" ), New Column( "BPN 3 Sample Mean" ) );
dtMeans << add rows( 100 );

For( i = 1, i <= 60, i++,
dt2 = dt << Subset( invisible, Sample Size( 3), columns( : BPN ) );

dtMeans:Sample[i] = i;
dtMeans:BPN 3 Sample Mean[i] = Col Mean( dt2:BPN );

Close( dt2, nosave );

);

Thanks!!

Re: Creating a Sampling Distribution

txnelson — Tue, 14 Jan 2020 12:30:00 GMT

The Subset platform has a built in random capability. Below is a simple script that uses

Tables==>Subset

to generate a random sample data table with 3 rows. It is in a For() loop, so you can specify to generate as many random samples as you want

dt = New Table( "test",
	New Column( "BPN",
		values(
			{103.2, 100.3, 99.2, 103.6, 102.1, 100.6, 100.1, 99.6, 99, 102.6,
			101.2, 97.6, 102.1, 100, 102.4, 101.7, 105.3, 103.7, 99.1, 103.1,
			99.3, 99.2, 98.5, 101.7, 106.3, 97.8, 104.6, 102.9, 103.1, 101.8,
			101.8, 99.9, 102, 100.6, 106.6, 100.6, 104.7, 98.4, 95.6, 103.2,
			103.5, 101, 102.8, 100.5, 97, 104, 99.8, 103, 103.4, 101.6, 100.6,
			101.9, 101.2, 99.7, 101.1, 101.1, 99.2, 104.9, 103.4, 106.4}
		)
	)
);

For( i = 1, i <= 10, i++, // change this line to produce as many subsets as you want
	dt << Subset( Sample Size( 3 ), Selected columns only( 0 ) )
);

Re: Creating a Sampling Distribution

nil — Thu, 16 Jan 2020 04:58:21 GMT

Thanks txnelson. The script output provides 10 random samples, each of sample size 3. As suggested, one can change required no of samples and or sample size. Script is limited to re-sampling (or random subset of sample size 3, 10 times).
Actually I would need script which can provide data table with mean of sample size 3, arranged in single column for lets say 10 random sample, which I would further use to understand probability of observing different mean values.

Re: Creating a Sampling Distribution

txnelson — Thu, 16 Jan 2020 05:12:23 GMT

Below is a simple modification of the script I previously responded with. The one below is just one of the ways to solve this. If you are going to play in the world of JMP Scripting, you need to read the JMP Scripting Guide, so you can start down the path of learning JSL.

names defalut to here( 1 );

dt = New Table( "test",
	New Column( "BPN",
		values(
			{103.2, 100.3, 99.2, 103.6, 102.1, 100.6, 100.1, 99.6, 99, 102.6, 101.2, 97.6, 102.1,
			100, 102.4, 101.7, 105.3, 103.7, 99.1, 103.1, 99.3, 99.2, 98.5, 101.7, 106.3, 97.8,
			104.6, 102.9, 103.1, 101.8, 101.8, 99.9, 102, 100.6, 106.6, 100.6, 104.7, 98.4, 95.6,
			103.2, 103.5, 101, 102.8, 100.5, 97, 104, 99.8, 103, 103.4, 101.6, 100.6, 101.9,
			101.2, 99.7, 101.1, 101.1, 99.2, 104.9, 103.4, 106.4}
		)
	)
);

dtSamples = New Table( "Samples", New Column( "Sample Means" ) );

For( i = 1, i <= 10, i++, // change this line to produce as many subsets as you want
	dt2 = dt << Subset( invisible, Sample Size( 3 ), Selected columns only( 0 ) );
	dtSamples << add Rows( 1 );
	dtSamples:Sample Means[N Rows( dtSamples )] = Col Mean( dt2:BPN );
	Close( dt2, nosave );
);

Re: Creating a Sampling Distribution

nil — Thu, 16 Jan 2020 05:24:43 GMT

Thank You!! Yes, I shall do the suggested on JSL learning.