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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) Descriptive 2) Inferential. Descriptive Statistics.

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Statistical Reasoning

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  1. Statistical Reasoning

  2. 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) Descriptive 2) Inferential

  3. Descriptive Statistics • Summarizesa set of raw data. • Many ways to organize the data: • Bar graph, line graph, pie graph, … • Tables • Illustrations • Statements

  4. Pie Graphs

  5. Line Graphs

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

  7. Abuse of Statistics

  8. 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

  9. 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

  10. 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)

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

  12. 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 withhighvariability, a summary becomes less reliable

  13. 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?

  14. 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

  15. 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

  16. Inferential Statistics • Otherwise… Low Reliability!

  17. 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

  18. 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?

  19. 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?

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