Download Statistics

STATISTICS
A way to organize data so that it
has meaning!
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Descriptive - Allow us to make observations
about the sample. Cannot make conclusions.
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Inferential – Allow us to generalize our findings
from the sample to the population. Allow us to
make conclusions.
LEVELS OF DATA
Nominal – used to name or categorize
 Ordinal – used to rank
 Interval – consistent units of measurement,
equal spacing, no true zero point
 Ratio – same as interval, but with true zero
point.
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DESCRIPTIVE STATISTICS
Measures of Central Tendency
Measures of Dispersion
MEASURES OF CENTRAL TENDENCY
Describe “typical” score in a distribution
 Mode, median, mean
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MODE
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Most frequently
occurring number in
data set
*only measurement of
central tendency that
can be used with
nominal level data
If there are 2, call this
a bimodal distribution
MEDIAN
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Rank data
ascending/descending
order and find the “middle”
number.
Best indicator of central
tendency when there is a
skew b/c it is unaffected
by extreme scores
If n is odd, will be whole #
If n is even, will be
between two values
MEAN
Arithmetic average of a set
 Requires interval or ratio data
 Sum of all scores/n
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 x1
+ x2 + x3+…xn / n
 n = sample size
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Problem: Always pulled towards extreme
scores or any skew of a distribution
 Look
at standard deviation to help understand how
far away most scores are from the average.
WHY DO WE NEED TO CALCULATE THE MEAN,
THE MEDIAN AND THE MODE?
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If they are all similar,
you have very little
distortion/skew!
If both the median and
mode are to one side of
the mean, your data is
skewed or distorted!
GRAPHS ALLOW US TO QUICKLY
SUMMARIZE DATA
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Bar graph
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Height of bars indicate % or
frequency
Titles and axis must be
labeled to reflect the aim of
the study!
MEASURES OF DISPERSION
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Amount of spread/variability in data
distribution
 How
close is each individual score to the overall
mean?
RANGE
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Distance between top and bottom values of a set.
Not for nominal numbers!
Advantages: easy to calculate
Disadvantages:
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distorted by extreme scores misleading
Doesn’t tell us if the values are closely grouped around the
mean or equally spaced across entire range
STANDARD DEVIATION
The average of how far the scores are from the
mean
 Requires interval or ratio level data
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STANDARD DEVIATION = (S)
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Find mean of data set
Subtract mean from each value = deviation
(d)
Square each (d)
Find the sum of d2
Divide step 4 by (N-1)
Take the square root of this number!
STANDARD DEVIATION = (S)
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This tells you how far
away (on average) the
scores are from the
mean in the sample.
The larger the standard
deviation, the more
variability in your data.
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The less you can trust
your mean score to be an
accurate representation
of a typical score!
TI 80 MILLION MAGIC!
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Clear lists
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Enter your data
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Stat button
4: clear list
2nd function, 1 (for L1)
Enter…screen will say “done”
Stat button
Cursor will be on 1: edit, hit enter
Enter your data into L1, hit enter after each number
Magical calculation!
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Stat button
Arrow over to Calc
Cursor will be on 1: 1-Var Stats, hit enter
Screen will say “1-Var Stats”
2nd 1 (to tell it which list you want it to calculate from ) and hit enter
MAGIC!!!
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Sx = standard deviation
TI-SOMETHING MAGIC!
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On
Clear your list
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Enter your data
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Stat button
1: 4 clear list
2nd 1 (L1)
Enter (done)
Stat button
1: Edit
Enter data into L1
Magically calculate all of your descriptive stats!!!
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Stat button, arrow to calc
1: 1-Var Stats
2nd 1 (L1)
Enter
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Will list LOTS of numbers (mean, median, mode & Sx =standard deviation)