1. Teaching Statistics in Psychology
UTOPPS—Fall 2004
Teaching Statistics in Psychology

2. AP Psychology “Suggestions”
Descriptive Statistics
Measures of central tendency
Variability
Correlation
Experimental Design
Appropriate Sampling
Control

3. Measures of Central Tendency
Mean
True average
Median
True middle of sorted data
Mode
Most frequent data value

4. How these measures relate
In a normal distribution…
Mean = Median = Mode
In a nonnormal distribution (one that is skewed)…
The mean will be impacted by the unusual values and will be pulled toward the skew.

5. Examples

7. Which measure do you use?
If the distribution is close to normal, they are all equal and it makes no difference
If the distribution is skewed, the median is the best measure of center because it is “resistant” to influence from outliers that cause the distribution to be skewed.

8. Variability Variation occurs Range of the data (max-min)
there may be a center to the data, but each individual value will vary around that center
Range of the data (max-min)
Quartiles (divide the data into quarters)
Interquartile Range (Q3 – Q1)
Standard Deviation
Average distance that a data point lies away from the mean
As a rough estimate—figure out the distance that each data value lies from the mean, and take the average
Not an exact calculation, but it gives a rough idea.

9. Practicing Calculations
1,1,2,3,4,5,6,7,8,9,10,16
Median (easiest)
5.5 (average between 5 and 6)
Mean
Add ‘em all up and divide by 12 6
Mode
1 (occurs most frequently)

10. More Practice 1,1,2,3,4,5,6,7,8,9,10,16 Range Quartiles
16 – 1 = 15
Quartiles
Medians of the lower and upper halves
Q1 = 2.5
Q3 = 8.5
Interquartile range
Q3 – Q1 = 6

11. Standard Deviation
1,1,2,3,4,5,6,7,8,9,10,16
The formula for standard deviation is quite complicated, but we will use a procedure to estimate this value.
The mean value is 6
The differences between each data point and 6 are all follows:
-5, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 10
Square those differences, add them all up and divide by 12 and then square root.
( )/12
Square root your answer

12. When to use Standard Deviation
Standard deviation (like the mean) is impacted by unusual values, so should not be used unless the distribution is close to normal.
If the distribution is normal, standard deviations are an excellent way to see how variability within the data.

13. Empirical Rule

14. How to interpret and use standard deviations
More than three standard deviations away from the mean is unusual, not impossible
If you see a result like this, we attribute that to mean that something unusual is occurring
We sometimes use this as evidence against the current mean
We sometimes use a p-value to indicate how unusual this result is
Something is considered unusual if the p-value is small (p < .05). Look back at the empirical rule slide…

15. Z-scores
Measure the number of standard deviations that a data point lies from the mean
If z is negative, the data point is below the mean
If z is positive, the data point is above the mean
Z = (data point – mean) / st. dev
If z is more than 2.5, then it is considered unusual in most settings

16. AP Psych Exam 2003
Statistics are often used to describe and interpret the results of intelligence testing.
Describe the three measures of central tendency
Describe a skewed distribution
Relate the three measures of central tendency to a normal distribution
Relate the three measure of central tendency to positively skewed distribution

17. An intelligence test for which the scores are normally distributed has a mean of 100 and a standard deviation of 15. Use this info to describe how the scores are distributed.
In two normal distribution, the means are 100 for group I and 115 for group II. Can an individual in group I have a higher score than the mean score for group II. Explain.

18. Correlation between two quantitative variables
Correlation is not Causation
Correlation shows that some linear relationship exists.
Correlation Coefficient
-1 < r < 1
-1 shows a very strong negative relationship
1 shows a very strong positive relationship
0 shows no correlation between the variables

20. Correlation between categorical variables
Difficult to assess
Comparing percentages can be misleading
Bar graphs can be misleading