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STATS
TO DETERMINE WHAT IS
NORMAL!!
2 TYPES OF STATS
DESCRIPTIVE – SUMMARIZES A SET
OF DATA
 INFERENTIAL – INTERPRET DATA
AND DRAW CONCLUSIONS
 (What can we infer about the
population from data gathered by the
sample?)

Example
EXAMPLE – In a recent study
volunteers who had less than 6 hours
of sleep were 4 times more likely to
answer incorrectly on a science test
than were participants who had at
least 8 hours of sleep.
 Which part is descriptive? Inferential?

Graphs

TO GET A BETTER SENSE OF DATA,
INFORMATION CAN BE PUT ON
HISTOGRAMS – BAR GRAPHS OR
FREQUENCY POLYGONS – LINE
GRAPHS
MEASURES OF CENTRAL
TENDENCY
MEAN
 MEDIAN
 MODE
 REPRESENT WAYS TO SUMMARIZE
DESCRIPTIVE STATISTICS

Misleading
Suppose your Mom wants you to
attend a family reunion on Sunday
 Everyone in the family protests
 Your Mother attempts to separately
convince each family member that it
will not be so bad

Mom
Mom tells your younger sister that the
average age is 10
 She tells you the average age is 18
 She tells your Dad it is 36
 Everyone feels better about going
 Did Mom lie?

Attendees
Attendees’ ages
 3, 7, 10, 10, 15, 17, 18, 44, 49, 58, 59,
82, 96
 What is the mean, median, mode?
 Did Mom lie?

NORMAL DISTRIBUTION





BELL SHAPED CURVE
POSITIVELY AND NEGATIVELY SKEWED –
DIRECTION OF THE TAIL
The tail tells the tale!!!
EXAMPLE – POSITIVELY – ALL STUDENTS
FAIL A QUIZ AND 2 MAKE 100’S
NEGATIVELY – ALL STUDENTS MAKE
“A’s” ON A QUIZ AND 1 FAILS
MEASURES OF VARIABILITY
DESCRIBES THE SPREAD OF
SCORES
 INCLUDES: RANGE, STANDARD
DEVIATION, AND VARIANCE (SD
squared)
 RANGE – LOWEST SCORE
SUBTRACTED FROM THE HIGHEST
 SD – SQUARE ROOT OF THE
VARIANCE

Variability
If you collected the ages of all
students in the 11th grade there would
be little variability.
 If you collected the shoe sizes of all
students in the 11th grade there would
be greater variability.
 One outlier can greatly affect the
range.

SCORES
Z SCORES – THE MEAN SCORE OF A
DISTRIBUTION HAS A Z SCORE OR
STANDARD SCORE OF ZERO.
 1 STANDARD DEVIATION ABOVE
THE MEAN HAS A Z SCORE OF 1.
 ANOTHER TYPE OF SCORES ARE
PERCENTILE SCORES – AT OR
BELOW A PARTICULAR SCORE

CORRELATION
RELATIONSHIP BETWEEN 2
VARIABLES
 CAN BE POSITIVE – ONE VARIABLE
INCREASES AND THE OTHER
INCREASES
 NEGATIVE – ONE VARIABLE
INCREASES AND ONE DECREASES
 NONE - ZERO

Examples
How is studying related to grades?
 How is playing video games related to
grades?

SCATTERPLOTS

ILLUSTRATE THE STRENGTH AND
DIRECTION OF CORRELATIONS
CORRELATION COEFFICIENT
VARIES FROM -1 TO +1.
 STRENGTH OF RELATIONSHIP IS
SHOWN BY THE COEFFICIENT.
 CLOSER TO -1 OR +1 – THE
STRONGER THE RELATIONSHIP
 A NONE OR ZERO CORRELATION
HAS NO RELATIONSHIP

INFERENTIAL STATS

CAN WE GENERALIZE FROM A CHOSEN
SAMPLE TO THE LARGER POPULATION?
 P – VALUE – INDICATES STATISTICAL
SIGNIFICANCE
 LESS THAN 1 IN 20 PROBABLITY OF
BEING CAUSED BY CHANCE .05

Lower the p value - the more
significant