To Notes

IT 223 -- 1/5/11

Review Problems

1. Matching:

   a. Fisher	i. First Stated the Central Limit Theorem
   b. Cotes	ii. Tried to find the "ideal man" that nature was trying to produce
   c. Tukey	iii. Was the first demographer.
   d. de Moivre	iv. Coined the term "exploratory data analysis."
   e. Pascal	v. Father of modern statistics.
   f. Gauss	vi. First described the least squares method.
   g. Graunt	vii. First studied the theory of errors applied to astronomy.
   h. Galton	viii. First applied the theory of probability to gambling.
   i. Quetelet	xi. Introduced the concept of correlation.

   Ans: a. v; b. vii; c. iv; d. i; e. viii; f. iv; g. xi; h. iv.

2. Why is it important for a clinical trial to be randomized and double blind?

   Ans: Randomization equalizes all the effects other than the treatment being studied. Examples of these other effects for the Salk polio vaccine test are socio-ecomonomic class, genetic differences, behavior patterns, nutrition. A double blind experiment insures that the treatment is not biased towards the vaccine due to the placebo effect: people's mental state improves if they think they are receiving medicine, even if the "medicine" is a placebo. A double blind experiment can also guard against bias against the vaccine because it will prevent people from thinking that they are immune to the disease by keeping them from going to places where they might get infected like swimming pools.

3. What is the difference between a controlled experiment and an observational study?

   Ans: A controlled experiment is randomized, whereas an observational study is not. This means that the results of an observational study may be confounded by other effects called lurking variables.

4. Give examples of categorical, ordinal, and continuous variables.

   Ans: Categorical: gender, is a smoker, race, treatment group, occupation; examples of ordinal: year in college, response (1 to 5) on questionaire, skill level, seat category in an airplane (coach, business class, first class); continuous: height, weight, age, gpa, midterm score, SAT score.

5. What does SPSS mean?

   Ans: Statistical Package for the Social Sciences. PASW means Predictive Analytics Software.

Stemplots

• To summarize the various value of a univariate dataset, tally marks are traditionally used. Here are the sorted hypothetical exam scores:
  5  39  75  79  85  90  91  93  93  98

• Here is the tally diagram:

  

• A more informative technique is the stemplot, also called the stem-and-leaf display.

  95 | 8
  90 | 0133
  85 | 5
  80 | 
  75 | 59
  70 |  
  65 |
  60 |
  55 |
  50 |
  45 |
  40 |
  35 | 9
  30 |
  25 |
  20 |
  15 |
  10 |
   5 | 5
   0 |
  

  The last digit of each observation is recorded to the right of the vertical line down the middle, which is the "stem."

• See the document Histograms

• A histogram drawn with bins of equal width is also called a vertical bar chart.

Quartiles

• The Quartiles divide the sorted dataset into fourths.

• Q0 is the minimum point in the dataset. Approximately 0/4 (none) of the data are less than than Q0.

• Q4 is the maximum point in the dataset. Approximately 4/4 (all) of the data are less than than Q4.

• Q2 is the median (middle point) of the dataset. Approximately 2/4 = 1/2 of the data are less than than Q2. If the dataset has an even number of observations, the Q2 is the average of the middle two observations.

• Q1 is the median of the bottom half of the data. (If the dataset has an odd number of observations, the bottom half of the data contains the middle observation). Approximately 1/4 of the data are below Q1.

• Q3 is the median of the top half of the data. (If the dataset has an odd number of observations, the top half of the data contains the middle observation). Approximately 3/4 of the data are below Q3.

• Q1, Q2, and Q3 and also called the 25th, 50th, and 75th percentiles, respectively.

• Exercise: Find the quartiles of the hypothetical exam scores:
  5  39  75  79  85  90  91  93  93  98

• The interquartile range (IQR), is defined as
  IQR = Q3 - Q1.

• Here is a brief discussion of the method that SPSS uses to compute percentiles:
  www.childrenssmercy.org/stats/08/ComputingPercentiles.asp

  SPSS uses interpolation instead of the midpoint to find the final percentile.

• There are at least different eight methods for computing precentiles.

Boxplots

• The boxplot was popularized by John Tukey.

• A boxplot is a graphical representation of the quartiles of the data, plus any outliers.

• See the document Boxplots and Outliers.

Using PASW/SPSS

• Use SPSS to complete Project 1.

• Select Analyze >> Descriptive Statistics >> Explore to obtain the requested statistics and plots.

• Check the Percentiles checkbox to obtain Q1, Q2, and Q3 using the Tukey's Hinges method.

• Use the Brief SPSS Tutorial for more details.