Statistical Reasoning

Statistics

Allows psychologists to organize, summarize, and make inferences from data

Arranging data in a way that helps us see and interpret what our eyes would otherwise miss

2 Main types: 1) Descriptive2) Inferential

Descriptive Statistics

Summarizes a set of raw data. Many ways to organize the data:

Bar graph, line graph, pie graph, … Tables Illustrations Statements

Pie Graphs

Sales

1st Qtr2nd Qtr3rd Qtr4th Qtr

Line Graphs

Season 1 Season 2 Season 3 Season 40

2

4

6

8

10

12

14

Player 3Player 2Player 1

Illustrations, Statements

“The average family has an income of $70,000.”

Abuse of Statistics

Measures of Central Tendency

= locates the “center” of a set of values i.e. a summary of all the values

1. Mode Most frequently occurring score

2. Mean The calculated average score

3. Median The middle score; the 50th percentile

Measures of Central Tendency

Each method may give a different number

15, 20, 21, 36, 15, 25, 15

What are the measures of central tendency?

Mode: 15 Mean: 21 Median: 20

Measures of Central Tendency

can be misleading when used to summarize data

Example: in 1996, 66% of the NBA’s 411 players made less then the mean salary ($2.24 million) The mean was inflated by a few players

salaries (Michael Jordan - $33.14 million)

Misrepresentation

“The average family has an income of $70,000.”

Variation

We also need to know about the amount of variation in a data set

Standard deviation = a measure of the variability in a set of data Tells us if information is packed close

together, or widely dispersed For a data set with high variability, a

summary becomes less reliable

Variation

Example: Two basketball players have the same mean of 15 points per game. Player 1 always scores between 13 and 17 points per game, while player 2 scores anywhere from 5 to 25 points per game.

Would you be more confident predicting the number of points in the next game for player 1 or player 2?

Inferential Statistics

Uses data to learn about a population that the data might represent but not the actual participants studied

Allows researchers to draw conclusions from their study Such as: measuring the likelihood of a

particular behavior given a set of circumstances

Inferential Statistics

In order to generalize from a sample, there are three principles that must be satisfied:

1) All samples are representative of the pop’n

2) Observations have a low variability (low standard deviation score)

3) Many cases or trials have been studied

Inferential Statistics

Otherwise…

Low Reliability!

Statistics

Most of the time, both descriptive and inferential statistics are used. Descriptive: summarize the data,

organizes information so it can be interpreted easier, visually illustrate trends.

Inferential: draw conclusions about an entire pop’n, generalize, answer questions, inform theories

Critical Thinking Question:

The registrar’s office at the University of Michigan found that usually about 100 arts students have perfect marks by the end of their first term. However, only 10-15 students typically graduate with perfect marks.

How can we explain data trend?

Activity

Find a graphic or advertisement in a magazine or pop-culture media source (can use internet).

How has the author used (or abused) statistics to make a point?