Chapter 3 Flashcards
Descriptive statistics and the Normal distribution
Descriptive statistics
provide you with mathematical summaries of performance and performance characteristics
Taxonomy of measurements
lowest - nominal
highest - ratio
Nominal
a nominal scale is categorical in nature
- football positions
- gander
- type of car
There is no notion of order, magnitude, or size. Everyone within the group is assumed to have the same degree of the trait that determines their group.
Ordinal
- ranking, as the finishing place in a race.
- things are ranked in order, but the difference between ranked positions are not comparable.
Continuous
- interval
- ratio
numbers are said to be continuous in nature if they can be added, subtracted, multiplied, or divided and THE RESULTS HAVE MEANING.
Interval numbers
- temperature or IQ
- a value of zero simply represents a point on a number line. It doesn’t mean that something doesn’t exist
Ratio numbers
- have an absolute (true) zero
- weight or time
Only INTERVAL AND RATIO numbers can be subjected to mathematical operations
True
N
number of cases
X (like x1 or x2)
any observed variable that you might measure
the capital Greek letter sigma
the sum of
Frequency distribution
a method of organizing data that involves noting the frequency with which various scores occurs
- norm-referenced comparison
Percentile
is obtained by summing the present of scores that fall at or below the percentile you are calculating
- a percentile represents the present of observations at or below a given score
Example: if you achieved at the 90th percentile (P90), this simply means that your grade is higher than 90% of the people were tested.
Central tendency
its where the scores tend to center
Measures of central tendency
- mean
- median
- mode
Mean
the arithmetical average, the sum of the scores divided by the number of scores
- the most stable one
Median
- the middle score/ 50th percentile
- the most typical score in the distribution
Mode
- the most frequent observed score
- the most unstable measure of central tendency
- but the most easily obtained one
Skewness
the statistical term for the shape of a distribution
Positive skewness
distribution has a tail toward the positive end (RIGHT) of the number line
Negative skewness
distribution has a tail toward the negative end (LEFT) of the number line
Kurtosis
the peakedness of a curve
Mesokurtic
the normal curve (an average amount)
Platykurtic
- the flatter curve
- has a negative kurtosis value
Leptokurtic
- the steep curve (peaked)
- has a positive kurtosis value
Variability
the spread of a distribution of scores
Measures of variability:
- range
- variance
- standard deviation
Range
the high score - the low score
THE LEAST STABLE MEASURE OF VARIABILITY
Variance (S2)
a measure of the spread of a set of scores based on the squared deviation of each score from the mean
THE MOST STABLE MEASURE OF VARIABILITY