How to solve any statistics problem

I was grading the quizzes from my Advanced Quantitative Data Analysis class. This is a class of really smart people in a doctoral program at a selective university. And yet, some of them still had problems with the quiz. Therefore, in however many parts I feel like doing, I am going to discuss how to solve any statistics problem.

#1 CHILL !

Sun bathing in TunisiaI mean this most seriously. Often, I see people make mistakes because they panic, think they can’t do it, underestimate themselves and think, “The problem cannot be that easy”.

Here is an example:

For 17 girls diagnosed with anorexia, weight change after family therapy was as follows:

11,11, 6, 9, 14, -3, 0, 7, 22, -5 , -4, 13, 13, 9, 4 , 6, 11

Partial results are shown below. Fill in the missing results:


Lower C.L. Upper C.L. t-value df 2-tail Sig
3.60 .0007


What is it you are asked to do in the problem? You need to find the upper confidence limit for the mean, the t-value and the degrees of freedom.

What are the degrees of freedom for a t-test?

A single sample: There are n observations. There’s one parameter (the mean) that needs to be estimated. That leaves n-1 degrees of freedom for estimating variability. “

The degrees of freedom when you are estimating the mean with one sample is N-1, or  17-1, which is 16.

To understand a problem, look at the numbers you DO have.

  • You have the lower confidence limit.
  • You have all of the individual scores
  • You know the number of scores (17)

Think about what you DO know (or can look up in a textbook)

  • The mean is the sum of the scores divided by the number of scores
  • The lower confidence limit is the obtained mean MINUS (t * standard error).
  • The UPPER confidence limit is the obtained mean PLUS (t * standard error).



There are a number of ways to find the upper confidence limit but all involve adding the value of (t*standard error)  to the mean. With what you have from #2, I’d think the easiest strategy is

  • Find what the mean is
  • Find the difference between the lower confidence limit and the mean
  • Add that number to the mean

This is often the step where people have trouble. I think it comes from three missteps. One is that they are too stressed out. The second is they don’t relax a minute and think about what they DO know first. The third is that they don’t relax a minute and think about what is the right strategy. In short, I think most people (and I am as guilty of this as anyone) don’t spend enough time on the first three steps before jumping right to number four.

#4 DO IT

Carry out your strategy.

  • The mean is 7.29
  • 7.29 -3.6 = 3.69
  • Add 3.69 to 7.29  to get 10.98

That’s your answer.


Do a reality check. The mean is 7.29 . If it doesn’t fall between your upper and lower confidence limits, you did something wrong.

Check back tomorrow for further proof that these steps can be applied to any statistics problem (and any math problem – maybe any problem in life. )

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