Statistical Reasoning
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Transcript of Statistical Reasoning
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Statistical Reasoning
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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
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Descriptive Statistics
Summarizes a set of raw data. Many ways to organize the data:
Bar graph, line graph, pie graph, … Tables Illustrations Statements
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Pie Graphs
Sales
1st Qtr2nd Qtr3rd Qtr4th Qtr
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Line Graphs
Season 1 Season 2 Season 3 Season 40
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Player 3Player 2Player 1
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Illustrations, Statements
“The average family has an income of $70,000.”
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Abuse of Statistics
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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
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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
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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)
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Misrepresentation
“The average family has an income of $70,000.”
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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
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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?
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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
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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
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Inferential Statistics
Otherwise…
Low Reliability!
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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
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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?
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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?