Psychology 320: Psychological Statistics

Professor: Howard B. Lee

Lecture Notes

Week 1: Introduction, Chapter 5

Lecture 1

Review of material from previous statistics courses :

The Measure of Central Tendency (Average) is the middle portion of a distribution.

1. The Mean is the arithmetic average of the scores ( a.k.a. the "arithmetic mean"). It is equal to the total of all values divided by the number of values.

2. The Median is the score that divides the numerical distribution in half,where 50% of the values fall below and 50% fall above.

3. The Mode is the most frequently occurring value.

What is the difference between ...

1. Grade Point Average
   
2. Average Salary
   
3. Average Tax Payer
   
4. Batting Average
   

Which one are they referring to?
Mean and Median must be numerical (quantitative) data.
Mode can be numerical or nonnumerical (qualitative) data.

*The measure of central tendency that we usually refer to in class (and in statistics in general) is the arithmatic mean or simply "the mean".

The mean is subject to distortion by outlying values or "outliers".

Ex. For the values 1.,2.,3.,4.,10,000., finding the arithmetic mean will illustrate the effect of the outlier value of 10.000.
1+2+3+4+10,000 = 10010
10010/5 = 2002.
The mean is pulled towards the outlier.
*The median is a better measure of a central point.

Skewness

Departure from symmetry. The distribution with extreme scores at one end.

Where is the outlier? To the right when it is a positively skewed distribution.
The long tail tells you where the skew is.
A tail pointing to the left is a negatively skewed distribution.
A tail pointing to the right is a positively skewed distribution.

What is the mode in 1.,2.,3.,4.,10,000. ?
It doesn't exist! (This is the problem with using the mode).

Measure of central tendency can be manipulated to describe the distribution of data in particularly pointed ways.
For ex. The LAUSD Union and the LAUSD Management can manipulate the same data in a given distribution to their own advantage by using different measures of central tendency. The union claims that the average salary of teachers in LAUSD is lower than the national average by using the mode. The management claims that the average salary of LAUSD teachers is higher than the national average by using the mean.

Both sides are telling the truth. How is this possible? They are using different measures of central tendency.
Both sides should be using the median.
What is the average eye color ?
For ex. blue, brown, brown, green.
The average eye color is brown.
How did we compute this? By using the mode.

Who is the most popular candidate?
For ex.

Candidates	# Votes
A	36
B	52
C	18

The most popular candidate is B.
How did we compute this? By using the mode.

Frequency (categorical) data is often used in politics.

How are the following two sets of data different?
set # 1 : 1,2,3,4,5 mean = 15/5 = 3
set # 2 : 0,0,0,0,15 mean = 15/5 = 3
set # 3 : 3,3,3,3,3 mean = 15/5 = 3

Set # 1 has no mode. Set # 2 has a mode of 0. The distribution of data in the three sets is very different.

Measures of Variability How do these scores change from one another with respect to the average value?

Measures of Central Tendency	Associated Measure of Variability
Mean	Standard Deviation
Median	Semi-interquartile Range
Mode	Index of Dispersion

*For this course, 90% of the time we will be looking at the average and standard deviation.

In the book entitled "Contact in the First Four Minutes" about first impressions, the author states that the first impression sets the pattern for whatever follows. It is extremely important to be accurate the first time!

Lecture 2