Statistical Learning and Inference Methods for Reasoning ...
Statistical Reasoning
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Transcript of Statistical Reasoning
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?