Introduction to the Wonderful World of Statistics

1
Introduction to the Wonderful World of Statistics

• OK its not that wonderful but, its not that
  bad either.

2
The Wonderful World of Statistics FAQ

• Why study statistics?
• Numbers dont lie..
• but people lie with numbers.
• Better Question What are statistics?
• Measurement Tools
• They organize, summarize, generalize, and measure
  the REAL WORLD.

3
The Wonderful World of Statistics FAQ
Mean is 45
One standard deviation 5
Score is 48
Question How many standard deviations is the
score away from the mean?
Above or Below?
Question Calculate the Z score!
z lt/-gt
4
The Wonderful World of Statistics FAQ
Mean is 45
One standard deviation 5
Score is 48
Question How many standard deviations is the
score away from the mean?
Above or Below?
Question Calculate the Z score!
z - 23.8
The score
is
standard deviations
______
the mean.
5
The Wonderful World of Statistics FAQ
Question What is the center of these numbers?
6
The Wonderful World of Statistics FAQ

• Why psychological statistics?
• Statistics are just statistics anyone can (and
  often do) use the same ones.
• Psychologists use a particular styles questions.
  Therefore, there are particular measurement tools
  that psychologists use more often.
• Also, this is a users guide, not a programmers
  guide
• Programmers need to see the Statistics Dept.

7
The Wonderful World of Statistics FAQ

• Research Methods?
• Not necessary!
• Stats are blind to research methods.
• They assume you have already done good methods.
• They assume you know how to use them properly.

8
Hypothesis Testing

• Dont get scared! This is just a general
  overview! Just a preview of where we are
  headed Besides, most of you will find this
  completely logical today Then, you will
  abandon your knowledge the moment I put a formula
  on the board in a week or two.

9
Hypothesis Testing

• Given Information
• The national average for height is 68 (58)
• mnation 68
• Hypothesis
• The UB student average for height is 68
• mUB 68
• Yeah! What else could it be?
• Alt. Hypo There is something in the water.
• After all, WNY has historically been the East
  Coasts toxic waste dump.

10
Hypothesis Testing

• Question
• So, is the average height of UB students 68?
• Solution 1
• Measure everyone!
• Solution 2
• Take a sample.
• See if the sample average is 68

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Hypothesis Testing
Possible Sample Examples
Symbols ? Sample Mean n Sample Size
mUB 68?
Likely, if mUB 68
mUB 68?
Unlikely, if mUB 68
??
mUB 68?
12
The Journey

• How do we get the point that we know whether or
  not something has broken the less than 5
  chance rule

13
The Journey

• Task
• We have a drunkenness scale
• Ranges from 0-100
• Question
• Does two Rum Cokes produce higher drunkenness
  scores?
• The Journey
• What do we need to know about our scores after
  drinking two Rum Cokes?
• Im really asking? Please respond?

14
The Journey

• Central Tendency

• Measures of Central Tendency
• Mode
• Median
• Mean

15
The Journey

• Variability

• Measures of Variability
• Range
• Interquartile Range
• Varience Standard Deviation

16
The Journey
Shape
Normal
Skewed
Bimodal
17
The Journey

• How do we compare scores from different
  distributions?
• Common Measure
• Each score relative to the others in its group
• z - score

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The Journey

• The less than 5 chance rule?
• Question of probability
• Divide by the total number of possible outcomes?
• Need to know the probability of getting a sample!
• Need total number of possible samples.
• Sampling Distribution!

19
The Journey

• Other Issues
• Is there a chance that the decision was wrong?
• Say, a 5 chance.
• Error Types
• If mUB ? 68, then what does it equal?
• Estimation?
• What about
• Comparing two groups?
• Relationships?
• Non-normal distributions outliers?

20
The Journey
Hallo! said Piglet, what are you
doing? Hunting, said Pooh. Hunting
what? Tracking something, said
Winnie-the-Pooh mysteriously. Tracking what?
said Piglet, coming closer. Thats just what I
ask myself. I ask myself, What? What do you
think youll answer? I shall have to wait
until I catch up with it, said Winnie-the-Pooh.