Using G-Whiz Charts to Track Elusive Affirmations from Almost Adolescents
I have a 12-year-old son. This is not a unique condition. And you might think that I would be well prepared for the associated challenges, having been a 12-year-old son myself at one time. But you'd be wrong.
Regular readers of the blog might recall that my family and I recently moved from rural Central Pennsylvania to urban Sydney, Australia for 6 months. My son wasn’t too keen on the idea of leaving his friends and his dog behind to start 7th grade all over again in a new country. But his mother and I were confident that once we arrived, he would realize that we did, in fact, know what we were doing and that we were not, in fact, trying to ruin his life.
Australia is great. We've had many wonderful experiences and met many wonderful people here. My son is slowly warming up to the place, but he has still not completely bought into the idea.
I found myself missing the kind of positive affirmations that all parents hold dear, like "You were right, Dad," and "This is great, Dad," and "Maybe you're not as dumb as I thought you were, Dad." It seemed the frequency of such positive parental affirmations was low. I began to become concerned about my son's emotional health and wellbeing, and more importantly, how that reflected on me as a parent. Was my parenting process...out of control?
"Out of control." It’s an ugly phrase, and an even uglier reality. But how do you know for sure? Can you trust your casual observations? Or is there a more objective, perhaps more visual way to assess whether a process is out of control? A chart perhaps? But what kind of chart could possibly be used to track events as infrequent, as fleeting, as rare as compliments to a parent from a 12-year-old? If only there were a special kind of chart for monitoring such rare events. And then I remembered... Stat > Control Charts > Rare Event Charts!
Like any good parent, I am in the habit of recording every compliment I get from my son in a special notebook. He's only 12, but already the wealth of compliments I have received has nearly filled 3 pages of the miniature 3" x 4" pocket notebook that I keep with me at all times. (Wide-ruled, of course.) It occurred to me that a G chart might be the perfect way to evaluate the frequency of such positive affirmations, such glad comments, such exuberant utterances. Only for this purpose, I call it a "G-Whiz" chart, and I am sure it will be gracing the cover of Laudable Parenting magazine in no time. Look for it in your supermarket checkout, next to the National Enquirer and the Reader's Digest Joke Book.
In plotting these data (yes, I am tragically old-school, a throwback from a bygone day when data were plural), I decided to go back as far as November. (We moved December 31.) So in one column of my Minitab worksheet, I entered the dates—in order—of every affirmation I had recorded from November to the present (March 1st). Then I simply choose Stat > Control Charts > Rare Event Charts > G, entered the column under Variables, and clicked OK.
My suspicions were confirmed. The G chart below plots the number of days that passed between each positive affirmation from my son. Low points indicate a high frequency and high points indicate a low frequency.
I took heart in the fact that none of the points were above the upper control limit, which would mean that there was a significant decrease in the frequency of affirmations. I was also glad to see that many of the points were close to zero. In fact there was a whole string of zeros, and that made me really happy.
But then I had to remind myself that unlike most control charts, the x-axis on a rare events chart does not represent time, exactly, but rather observations. For example, on my G-Whiz chart, observations 21 to 26 were recorded over a period of 13 days. Observations 27 to 34, on the other hand, all occurred on the same day. A very special day as a matter of fact. A day when many 12-year-olds are often observed to be considerably happier and consequently more complimentary than most other days of the year. Christmas.
I thought about the fact that, by default, all observations are used to calculate the control limits on the chart. I realized that if I want the control limits to reflect the normal rate of affirmations, I probably did not want those calculations to include Christmas, or the subsequent period of frantic packing, or the sending of the dog to live with the sister-in-law in North Carolina, or the frequent scowls and chants of "I don't want to move to Australia," and "Why do you hate me?" and "I swear your hair looks more gray today than it did just yesterday, Dad."
If only it were possible to make all of that just go away. Fortunately, with a G-Whiz chart, you can.
I pressed Ctrl + E on my keyboard to reopen the G Chart dialog box. I then clicked G Chart Options and clicked on the Estimate tab. There, I chose Use the following subgroups when estimating parameters and entered "1:25" to indicate that I want the first 25 observations to be used to calculate the control limits.
It became even clearer from the modified graph (below) that Christmas—and the move—was followed by a significant "cold shoulder" period. Affirmations were at an all-time low as evidenced by the big red square soaring above the other points on the chart, and above the control limits.
It's worth noting that my G-Whiz Chart is somewhat unique. Not just because I'm measuring something as ephemeral as a compliment, but also because I am using the chart to measure good events. More often, a G chart is used to measure adverse events. When you measure something like hospital infections, for example, you want to see more points higher up on the plot, because that means the bad things are happening less frequently.
Another thing to notice is that with G charts, the lower control limit is usually equal to zero, which means that the points on the chart cannot fall below the lower control limit. So you need some other way to detect unusually high frequencies. That's why the Benneyan test is part of the default output in Minitab. The Benneyan test detects when a significant number of points in a row are equal to the lower control limit. Such points show up as red squares with a "B" next to them.
According to the Benneyan test, receiving 6 compliments on the same day is suspect and should be investigated. Observations 33 and 34 both represent a string of at least 6 zeros in a row. Of course, in this case we know that the special cause was Christmas.
With G charts and T charts, Minitab also includes Test 2 by default, which will alert you if 9 or more points in a row are on the same side of the center line. This gives you an even better chance of detecting a problematic change in the frequency of rare events. In my G-Whiz chart, you can see that there is a long string of points above the center line, where the frequency of affirmations remained low for a while. As a result, three points failed Test 2.
More recently, after a period of settling in, we've begun setting out and exploring Australia. And as my son makes friends and discovers new sports and other pastimes, the affirmation rate is again becoming stable. He feels better about Australia, and I can again sip coffee from my "World's Greatest Dad" mug with a smug sense of confidence.
It's good to be in control.