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		Lecture on Tukey chart
		Create Tukey chart using Excel
		Tukey chart Calculating limits Example: Exercise data Example: Budget data Which chart is right? Presentations Analyze data Recently asked questions More Minute evaluation
		Recently asked: To choose a tukey chart, you would choose it depending on whether outliers were likely. How would you know whether outliers were likely before creating the chart? I honestly do not think I would know when to use this chart. See answer to this and other questions.

Tukey Control Chart

There are many different types of charts. P-charts are useful for analysis of mortality data but assume large number of observations. X-bar charts are useful for analysis of satisfaction ratings but assume Normal data. We present here an approach based on Tukey’s exploratory data analysis techniques. The approach is robust and makes no assumptions regarding the distribution of outcomes plotted. We refer to this approach as Tukey's Chart.

In a control chart, you monitor progress over time. You create a plot, where the X-axis is days or weeks since start and the Y-axis is the outcome you are monitoring. To decide if your outcomes are different from historical patterns, the upper (UCL) and lower control limits (LCL) are calculated. These limits are organized in such a way as to make sure that if your historical pattern has continued then 99% of time data will fall within these limits. This section shows you how to calculate limits for Tukey charts - a type of chart useful for analyzing single observations per time period. )

Figure 1 shows the structure of a typical control chart. In this figure, all points, except for two, fall within the control limits.}

Figure 1: Components of a Control Chart

How to Read a Control Chart?

In a control chart, points outside the limits are unusual and mark departure from historical patterns. Two points in Figure 1 fall below the LCL and therefore mark a real change. All other points do not indicate any real change, even though there are lots of them showing a rise or fall. These fluctuations are random and not different from historical changes.

A control chart can be used to see if a process is stable, meaning that observations are falling within anticipated limits. If your data falls within the control limits, despite day to day variations, despite attempts to change the process, outcomes have not changed.

Minimum Number of Observations

The more data you have, the more precision you have in constructing the upper and lower control limits. At a minimum, you need at least 7 data points in the pre-intervention period to start a Tukey chart. This is an absolute minimum and not a recommended number. The actual number you need depends on the consequence of waiting and collecting more data versus using too little data and making an error in judgment.

Keep in mind that not all of the data you collect are used for calculation of control limits. Often, the limits are based on pre-intervention period. Then subsequent post-intervention observations are compared to the pre-intervention limits. When you make a change, you want to see if the change has affected the outcomes. In these circumstances, you set the limits based on the pre-intervention data. You compare post-intervention findings to these limits. If any points fall outside the limits, you may then conclude that the intervention has changed the outcomes. See Figure 2 for an example of limits set based on pre-intervention periods. The solid line shows the time period used to set the limit, the dashed line is an extrapolation of the limit to other periods.

Figure 2: Post-intervention data compared to limits set based on pre-intervention data

Compare the chart in Figure 2 with the chart in Figure 1. Both are based on the same data, but in Figure 2 the limits are based on the first 7 days, before the intervention. Figure 2 shows that post intervention data are lower than LCL and therefore a significant change has occurred. When Figure 2 is compared to Figure 1, we see that more points are lower than LCL in Figure 2. By setting the limits to pre-intervention patterns, we were able to detect more accurately the improvements since the intervention.

Control limits can be calculated from either the pre or the post intervention period and projected over to the other period. For example, control limits can be calculated from per-intervention period and extended to the post-intervention period. Or the reverse: control limits can be calculated from the post-intervention period and extended to the pre-intervention period. Either way, we are comparing the two periods against each other. But since the results will radically differ, it is important to judiciously select the time periods from which the control limits are calculated. The selection depends on the inherent variability in the pre- or post-intervention periods. Control limits are calculated from the time period with least variability. Typically, this is done by visually looking at the variability in the data or at the range of the data in pre- and post-intervention time periods. But in Tukey chart, outliers may appear to cause variability but do not affect the control limit calculations. Therefore, instead of visual tests or instead of looking at range of data, it is important to calculate the Fourth Spread (a concept explained in next section) and to select the time period with the smallest fourth spread. This will produce control limits that are tighter and more likely to detect changes in underlying process.

Figure 3 shows the control limits derived from pre-intervention data. The control limits are calculated from the pre-intervention period and shown as solid red line. They are extended to the post-intervention period, shown as dashed red line. The control chart compares the observations in the post intervention period to the control limits derived from the pre-intervention period.

Figure 3: Control Limits Derived from the Pre-Intervention Period

Figure 4 shows the control limits for the same data drawn from a post-intervention data. Note that this time around the control limits are calculated from the post intervention period, shown as solid red line. They are extended to the pre-intervention period, shown as dashed red line. The control chart compares the pre-intervention observations to the control limits calculated from the post-intervention data.

Figure 4: Control Limits Derived from the Post-Intervention Period

Note that both analyses are based on the same data. Both analyses compare the pre- and post-intervention data by contrasting the observation in one period to control limits derived from the other period. In one case, the control limits are drawn from the pre-intervention period and in the other from the post-intervention period. Note the radical difference of the control limits derived from the two time periods. The Fourth Spread (a concept explained in the next section) for the pre-intervention period is 10 points while for the post-intervention period it is 18 points. Figure 3 is the correct way to analyze the data, because it is based on the control limits derived from the pre-intervention period, the time period with smallest Fourth Spread. If control limits are based on the time period with the smallest Fourth Spread, they would be tighter and more likely to detect smaller changes in the underlying work process.

Calculating Limits

We will use Tukey’s suggested limits for calculation of confidence intervals. The procedure calculates control limits from difference of upper Fourth and lower Fourth of data, a concept that Tukey named Fourth Spread.

Most readers are familiar with median, a value where half the data are below and half the data are above it. A lower Fourth is similar to 25% quartile and is the median of the first half of the data. At this point, 25% of the data are below this value. An upper Fourth is similar to 75% quartile and is the median of the upper half of the data; at this point 75% of the data are below this value. The difference between the two Fourths is referred to as Fourth Spread. The Upper Control Limit is calculated as the sum of the upper Fourth and 1.5 times the Fourth Spread. The Lower Control Limit is calculated as the difference of the lower Fourth and 1.5 times the Fourth Spread.

Here are the procedure for calculating Tukey’s control limits:

List values from smallest to largest.
Calculate median, where 50% of data are below if and & 50% above it. If odd number of observations, take the value in the middle. If even number of observations, take average of the two middle ranked numbers.
Divide the data set into two halves using the Median. Include the Median in both halves if it Median is one of the observed data points.
Lower Fourth is the median of the lowest 50% of the data, data from the smallest number till (or including) the median.
Upper Fourth is the median of the top 50% of the data, data from (or including) median of the full data set to the highest value.
Calculate Fourth Spread as the difference between the two Fourths?
Calculate UCL and LCL using the following two formulas:

LCL = Lower Fourth - 1.5 * Fourth Spread

UCL = Upper Fourth + 1.5 * Fourth Spread

Example in Exercise Time & Weight Loss

Jane collected data in Table 1 regarding her exercise times. She planned to exercise 3 times a week and each time she exercised she recorded the time in minutes. When she did not exercise, she recorded a 0 for the length of exercise. The first 7 days recorded were pre-intervention. After this period, she and her spouse joined a mixed group volleyball team. The question she wanted to know was whether joining the team had made a difference in her exercise time.

Table 1: Length of Exercise
Day of observation	Minutes of exercise	Sorted in order of length of exercise
Day of observation	Minutes of exercise	Rank	Day of observation?	Minutes of exercise
1	30	1	2	0
2	0	2	3	25
3	25	3	1	30
4	30	4	4	30
5	35	5	5	35
6	40	6	6	40
7	50	7	7	50
8	45
9	31
10	20
11	40
12	60
13	45
14	60
15	45
16	32
17	50
18	60

We can calculate the control limits from the pre-intervention or post-intervention period. It so happens that the limits calculated from the pre-intervention period are tighter (meaning the difference of upper and lower control limit is smaller) and therefore the following shows how to calculate the control limits from the pre intervention period. While we focus on setting the limits from the pre-intervention period, in reality you should do it from either period and select the time period that produces the tighter control limits.

The first step is to sort pre-intervention data in order of length of exercise. This is shown in Table 1 in the last column of the Table. Next, we calculate the median, this is the value where ½ the data (7 * .5 = 3.5, 3 points) are below it and ½ the data (3 points) are above it. The 4^th data point with value of 30 is the median; 3 data points are below it and 3 above it.

Since median is an actual data point, we include this point in the lower data set. To calculate the Lower Fourth, we calculate the half way point for the first half of the data. When we include the median, we have 4 points in the lower data set. The 25% quartile is halfway between the second and third point, in other words between 25 and 30, which is 27.5.

To calculate upper Fourth, we calculate the half way point for the upper half of the data. Again because the median is an actual data point, we include this point in the upper dataset. With the median, we have 4 data points from Median to the highest values. The upper Fourth is between the 5^th and 6^th data points (between 35 and 40), and therefore its value is 37.5.

The Fourth Spread is the difference between the upper and lower Fourth, which is 37.5-27.5 = 10. The Fourth Spread for the control limits calculated from post-intervention data is 18 points and this is why we have selected to calculate control limits from pre-intervention data. The UCL is calculated as 37.5+1.5*10 = 52.5. The LCL is calculated as 27.5-1.5*10 = 12.5. A chart of the data is provided in Figure 5:

Figure 5: Tukey's Control Chart for Data in Table 1

Examination of the chart shows that in the first seven days, there was one very low point of no exercise, a statistical abnormality. After the first 7 days (used for setting the limits), on 3 occasions the total exercise time exceeded the UCL. In these three days, there was a real increase in exercise time compared to the first 7 days. If these days correspond to joining the volleyball team, then the intervention seems to have worked.

Let us look at another example, this time on weight loss. A male, 48 year old man measured his weight for 8 weeks. Then he and his spouse changed food shopping habits. They excluded all sweets from their shopping (they stopped buying pops, sweetened cereals, and chocolates for the house). The data for this person is provided in Table 2. Weight was recorded once a week.

Table 2: Recorded weight values
Week	Pounds over ideal weight	Sorted values
Week	Pounds over ideal weight	Rank	Pounds over ideal weight
1	9	1	3
2	11	2	5
3	7	3	7
4	7	4	7
5	10	5	8
6	5	6	9
7	3	7	10
8	8	8	11
9	6
10	6
11	3
12	0
13	4
14	-1
15	-5
16	-2

As before, we need to calculate the control limits for pre and post-intervention periods and select the limits with the smallest difference. It so happens that that the pre-intervention period has the smallest Fourth Spread and therefore we show the calculation of control limits from these data. The first step is to sort pre-intervention data from least amount of pounds over weight to the highest value. This is shown in Table 2 in the last column of the Table. Next, we calculate the median, this is the value where ½ the data (8 * .5 = 4 points) are below it and ½ the data (4 points) are above it. The value should be between 4^th and 5^th data points, or between 7 and 8, so the median is 7.5.

Since median is not an actual data point, we do not include this point in the calculations of Fourths. To calculate the lower Fourth, we pick the half way point for the first half of the data. We have 4 points in the lower data set. The Lower Fourth is halfway between the 2^nd and 3^rd point, in other words between 5 and 7, thus it is 6.

To calculate the Upper Fourth, we calculate the halfway point for the upper half of the data. Again because the median was not an actual data point, we do not include this point in the upper data set. We have 4 data points for the highest values. The Upper Fourth is between the 6^th and 7^th data points (between 9 and 10), and therefore it is 9.5.

The Fourth Spread is the difference between the Upper and Lower Fourth, which is 9.5-6 = 3.5. The UCL is calculated as 9.5+1.5*3.5 = 14.75. The LCL is calculated as 6-1.5*3.5 = 0.75. A chart of the data is provided in Figure 6:

Figure 6: Control chart for the weight data

Examination of the chart shows that in the first eight weeks, all data points were within the limit. No weight was lost in the pre-intervention period, even though there was considerable amount of fluctuations. Over the remaining 8 weeks and compared to the first 8 weeks, on 4 occasions the weight was lower than the LCL. Therefore, there was a real decrease in weight in the post intervention period.

Example in Medication Errors

The following data show the error in PYXIS refills in a hospital.

Name of Drug Refilled	Date of Error	Type of Error
Promethazine inj 25 mg	05/13/07	Wrong strength
Lidocaine 1% w/ Epi	06/13/07	Wrong strength
Ofloxocin Opth	05/14/07	Wrong dose form
Sensorcaine 0.25%	05/07/07	Wrong strength
Lidocain 1% w/ Epi	06/20/07	Wrong strength
Tramadol 50 mg tab	05/21/07	Wrong drug
Morphine Sulfate 30 mg	07/01/07	Wrong dosage
Table 3: Recent PYXIS Refill Errors

Note that there are no pre- or post intervention time periods and therefore the entire data can be used for calculation of control limits: To analyze this data we first calculate time between errors:

Date of Ending Incident	Days Between
5/13	6
5/14	1
5/21	7
6/13	23
6/20	7
7/1	11
Table 4: Days to Errors

Next we reorder the observations from lowest days between errors to highest dates: 1, 6, 7, 7, 11, and 23 days. The median for the data is 7. The upper fourth is the median of 7, 11 and 23 and thus it is 11. The lower fourth is the median of 1, 6, and 7 and thus it is 6. The fourth spread is 5 days. The upper control limit is the upper fourth plus 1.5 times the fourth spread which is 18.5. The lower control limit is a negative number and thus it is re-set to zero. Figure 7 shows the control chart:

Figure 7: PYXIS Refill Errors Improved from 5/21 to 6/13

Example in Budget Variation

Suppose that we are looking at 12 month of data regarding our clinic's budget. The question is whether the expenditures at any particular month are higher than the general pattern across the 12 months. The table below shows the budget deviation (expenditure minus budget amount) for each of the months in thousands of dollars:

Month	Budget deviation in 1000su
1	23
2	-5
3	-70
4	-7
5	-8
6	9
7	12
8	30
9	24
10	25
11	-4
12	-2

Note that there are no pre- and post intervention time periods and therefore the entire data are used for estimation of control limits. The first step is to sort the data:

Rank	Budget deviation in 1000
1	-70
2	-8
3	-7
4	-5
5	-4
6	-2
7	9
8	12
9	23
10	24
11	25
12	30

There are 12 data points, so the median is halfway between the 6th and 7th ranked data points. Therefore, the median is not included in the lower and upper data sets because it is not an actual value in the data. The Lower Fourth is halfway in between the 6 data points with lowest ranks, it is between 3rd and 4th ranked data points and has the value of -6. The upper data set is the points ranked 7 through 12. Median of this data set is halfway in between the 9th and 10th ranked data items. It is 23.5. The Fourth spread is 29.5.

The UCL is 23.5+1.5*29.5 and the LCL is -6-1.5*29.5. Figure 8 shows the control chart:

Figure 8: Tukey Chart for budget information (in 1000 of dollars)

The chart shows that all months are within control limits except for March, where in there has been a large deviation from the budgeted amount.

Which Chart is Right?

Figure 9: Tukey chart is best when there are single observations per time
period, outcomes are measured on an interval scale, and outliers are likely

When tracking data over time, you have a number of options. You could use a P-chart, designed specifically to track mortality or adverse health events over time. You could use a moving average chart to help you construct control chart for an individual patient's data over time. This section helps you decide which of these various charts are appropriate for your application. If you do not have a specific application in mind or if you wish to learn more about each of the various different charts, skip this section. In the following, we ask you 4-7 questions and based on your answers advise you which chart is right for the application that you have in mind.!

Have you collected observations over different time periods?

Yes

No

Analyze Data

Advanced learners like you, often need different ways of understanding a topic. Reading is just one way of understanding. Another way is through doing and practicing the concepts learned in this section. The following questions are designed to get you to think more about the concepts taught in this session.

Assume that following data regarding one patient's rating of his/her health status over eight time period:

Time period	1	2	3	4	5	6	7	8
Observations	90	85	92	67	98	83	94	90

Has the patient's health changed? Note that there are no interventions and therefore the entire data can be used to estimate the control limits.

Analyze the following data using Tukey, XmR and Time-In-Between (more than 30 minutes of exercise considered a successful day) charts. Produce 3 charts and discuss if the findings from the 3 charts are similar. To decide if the exercise time has changed, rely on the control chart with the smallest difference between upper and control limit.

Day	Minutes of exercise
1	25
2	30
3	32
4	0
5	15
6	17
7	15
8	40
9	15
10	28
11	0
12	60
13	20
14	24

How Will Your Assignment be Graded?

Correct answers are needed for each of the four charts. An error in any chart will constitute 25% of the grade.
All values must be computed as a formula except the data provided above. It should be possible to change the data and the graph should change. Submitting a file that does not do this will be counted as error in analysis. This means that you may have to use if, count, average, median and other functions. Do not under any circumstance enter the result of the calculation by hand.
Inappropriate displays will lose 10% of the grade for the chart, this means the following:
1. All lines must have a legend or have a label. No lines should be labeled "Series 1".
2. The UCL and LCL should be drawn as lines with no markers, preferably in red.
3. Observations must be drawn with markers connected with lines.
4. There must be a title to the chart and x and y axis should be labeled.
5. There should not be any spelling errors anywhere in the chart.
6. All charts must be shown in the same file. Do not email multiple files. Label worksheets.

Email Your Analysis

Email your instructor and obtain his email. Then send an email to him with your Excel file attached. For full credit of your work, in the subject line include the course number and your name. For example, subject line could be: "Joe Smith from HAP 586 analysis of data using Tukey chart" Please submit one file containing answers to all questions. Please note that all cell values must be calculated using a formula from the data. Do not enter values in any calculated cells. Calculate each cell using Excel formulas.

Presentations

To assist you in reviewing the material in this lecture, please see enclosed resources:

Tukey chart lecture Slides► Listen►
See an example in Excel Video► SWF► Excel 2003►

Narrated slides and video require use of Flash.

Frequently Asked Questions

Ask a question and we will answer it within the next 48 hours. If you have no questions, please review the answer to the questions asked by others:

Question: To choose a tukey chart, you would choose it depending on whether outliers were likely. How would you know whether outliers were likely before creating the chart? I honestly do not think I would know when to use this chart. Answer: You can look at the data and see if there is an outlier. This question was asked on 4/22/2008 10:07:29 PM and answered on 4/23/2008 7:38:38 PM.

Question: Without a pre and post intervention, how can you determine if any observations outside the LCL and UCL occured for reasons other than by chance? Answer: The same way that you can do so with pre/post intervention data. Any time points are outside control limit, whether the limit is based on portion of the data or all of the data, it indicates that a very low chance event has occured and therefore there is a good reason to beleive that the process is changing. This question was asked on 4/22/2008 1:19:35 PM and answered on 4/22/2008 6:59:42 PM.

Question: In class, you mentioned you would be checking the homework this week. Do you want us to send to you or you and Bathsheba? Answer: Yes please send to both. This question was asked on 4/21/2008 9:06:26 AM and answered on 4/21/2008 9:32:58 AM.

Question: For question 2, my tukey and XMR charts are coming up with negative numbers for the LCL. Must I make those numbers zero or is it reasonable to leave them as negative? Answer: If negative values are not possible, you must change them into zeros. This question was asked on 4/18/2008 12:48:54 PM and answered on 4/18/2008 3:36:37 PM.

Question: For Q2 on this week's data analysis assignment, both the turkey chart and the XmR chart had similarly tight control charts. When they are so close, how do you decide for sure which is the best to use? Thanks. Answer: If they are really close, you can go with either approach. This question was asked on 4/14/2008 11:47:49 AM and answered on 4/15/2008 11:49:27 PM.

Question: I realize that depending on what you are looking for and the type of data you have influences the type of chart....but isn't this also just a way to make the numbers say what you want them to say? Answer: You mean that we torture the data until they confess? :) Seriously, no. The choice of control chart methods often does not change the conclusions derived or makes slight changes in the conclusions. This question was asked on 11/27/2007 9:33:02 PM and answered on 11/28/2007 7:49:35 AM.

Question: For problem 2, how do I know what is pre- and post-intervention? Do I use the whole data set to calculate it? Answer: If the problem does not specify an intervention period, you have to assume that the entire data should be used to estimate the control limits. This question was asked on 11/27/2007 8:57:47 PM and answered on 11/28/2007 7:47:58 AM.

Question: How many times should an observation go above the UCL in order to confidently make an analysis that change has taken place overall? Answer: In 100 points, you would expect 1 point to be above the UCL drawn at 3 standard deviation away from mean. In fewer points you would expect none. So even one point signals a change in process -- perhaps a temporary change This question was asked on 11/27/2007 2:08:53 PM and answered on 11/27/2007 2:14:26 PM.

Question: The advantage of the Tukey chart is improved accuracy in determining effective change. Is that correct? If you have not implemented a change then you should not use a Tukey chart? Answer: All control charts measure if a process has changed. Tukey is specially advantageous because it is not affected by an occasional outlier. Medians are not affected by outliers while means are affected. This question was asked on 11/26/2007 9:33:56 PM and answered on 11/26/2007 10:20:28 PM.

Question: Can you give advice regarding using the "if" statement when trying to set a negative number to zero. Is there somewhere that explains the process in the notes/slides/etc? I can't seem to find it. Answer: I will put an example up so that you can see it in a video. Please check under Introduction to Excel for a video in a day from now. This question was asked on 11/25/2007 5:37:01 PM and answered on 11/25/2007 7:22:22 PM.

Question: Which chart is right? Answer: There are multiple ways to analyze single observations per time period. If you have continuous data, the choice is between XmR and Tukey. I prefer Tukey in situations where there are few time periods and therefore one can expect that an outlier could radically shifts the mean and standard deviation in XmR charts. In contrast, because Tukey works with medians, an outlier has no effect on calculation of control limits. If the data is dichotomous, I prefer to use time-in-between charts for rare events (e.g. missing medication). If the event being examined is not rare, then I prefer to use p-chart. For a more detail guide to which chart is right click here.

Question: What is the relationship between range and standard deviation? Answer: Both range and standard deviation measure the spread of a distribution. Range can be used to estimate the standard deviation. Standard deviation can be calculated as the average of moving range divided by a constant. This constant depends on the sample size. See a more details and a statistical answer to the question.

Question: What makes Tukey chart more robust? Answer: Tukey charts do not make any assumptions regarding the distribution of the observations. Because the control limits are based on quartile values, they are less likely to be affected by outliers.

Question: How do you calculate quartile values in Microsoft Excel? Answer: Use the function Quartile(range, n), where n is either 1, 2,3, or 4. When n is 1, this function produces the 25% quartile. When n is 3, it produces the 75% quartile.

Question: In calculating quartiles using Excel functions, I get a different answer than following procedures described here. Why and which is right? Answer: When a quartile falls between two observed values, Excel calculates this quartile value proportional to the percent of data that fall below or above the quartile. For example, in a 75% quartile that falls between two values, the quartile is estimated to be 75% above the lower value and 25% below the higher value. In contrast, we take a mid-point, thus our answers and Excels answers differ for quartiles that do not fall on an exact values. The question is which is right and when to use which approach? If you are calculating quartiles using hand calculations, follow the procedures described here. If you have access to Excel, use the Quartile function of Excel. For a detailed and understandable description of the algorithm used by Microsoft Quartile function click here.

Suggestions for Improving "Tukey Chart"

Add your own suggestions or read below suggestions made by others regarding how to improve this session:

Comment: The video showing process of creating tukey chart was great. This comment was left on 7/4/2009 1:34:42 PM.

Comment: Making the storyboard was fun, and it was nice to see everything we went through and combining it together. Tukey Chart was the hardest, and honestly I still do not know how to complete it. This comment was left on 7/3/2009 11:41:34 AM.

Comment: At first I had some confusion with the definition of the figures between the website and the book. Figure six in the book and figure 6 on the website are different. This comment was left on 6/28/2009 11:42:45 PM.

Comment: This was by far the most effort I put in an assignment, it was because I did a Tucky's chart from my own data and not from the given data in the web page. Thankfully I understook what I was supposed to do. I learned a lot about excel from this topic, Thank you! This comment was left on 6/28/2009 10:40:29 PM.

Comment: I'm having trouble understanding what exactly we are expected to do. I think the instructions need to be more detailed This comment was left on 6/28/2009 9:17:42 PM.

Comment: I think a new video needs to be made for how to create a tukey chart b/c the new excel 2007 is very different and the video isn't 100% accurate. I did find the video helpful as well as the slide show. the chart does help to see the data more accurately. This comment was left on 6/28/2009 7:15:04 PM.

Comment: Comment on the storyboard session 7. Excellent guidance and coaching. This comment was left on 6/28/2009 6:08:15 PM.

Comment: During the last two sessions, not only did I learn more about systems analysis using my own data but I also learned how to use Excel 2007 by constructing control charts and tukey charts. Although, this was challenging at first. I managed how to figure it out by listening to the lectures and reading the chapter. This comment was left on 6/28/2009 11:38:18 AM.

Comment: I found this specific assignment a bit frustrating for me. I've done the chart several times and it just wouldn't come out the way it should be. The powerpoints didn't help me as much, this is my least favorite assignment This comment was left on 6/21/2009 10:50:22 PM.

Comment: I had to move my sound all the way up and still the lecture was barely audible. This comment was left on 6/21/2009 11:30:36 AM.

The collected work of John Tukey.
Tukey writes about exploratory data analysis.
Box and whisker plots or see related web sites.
Who was Tukey?
The Internet Glossary of Statistical Terms
Tukey's writing in health care.

This page is part of the course on Quality / Process Improvement, the lecture on "Tukey chart." This page was first prepared on January 1990 and last revised 09/29/2008. Copyright protected by Farrokh Alemi, Ph.D. © Copyright 2003. For a published version of this web page see: Alemi, F. Tukey's Control Chart. Quality Management in Health Care. 13(4):216-221, October/November/December 2004. Accession Number: 00019514-200410000-00004. See also criticism of the approach by Borckardt JJ, Nash MR, Hardesty Sue, Herbert J, Cooney H, Pelic C. An Empirical Evaluation of Tukey's Control Chart for Use in Health Care and Quality Management Applications. Quality Management in Health Care. 14(2):112-115, April/June 2005. Accession number 00019514-200504000-00006. Authors response to the criticism is available at Alemi F, Baghi H. Simulated Environment Is Not Appropriate. Quality Management in Health Care. 14(3):165-166, July/September 2005. Library membership is required to view these documents.