Transcript Basic Statistical Terms:

Basic Statistical Terms:
Statistics: refers to the sample
A means by which a set of data may
be described and interpreted in a
meaningful way.
A method by which data can be
analyzed and inferences and
conclusions drawn.
Population: All of the possible subjects
within a group.
Sample: A part of the population
Random Sample: Every member of a
specified population has an equal
chance of being selected
Ungrouped data: Raw scores presented
as they were recorded; no attempt
made to arrange them into a more
meaningful or convenient form
Grouped Data: Scores that have been
arranged in some manner such as from
high to low or into classes or categories
to give more meaning to the data or to
facilitate further calculations.
Frequency Distributions: A method of
grouping data; a table that presents the
raw scores or intervals of scores and
the frequencies with which the raw
scores occur.
Measures of Central
Tendency:
Mean: The arithmetic average
population mean = 
sample = X
Examples:
12
11
10
9
8
 x1 50
X
X= N
=
50
5
= 10
What is happening here?
30
11
10
9
8
X = 68
X 68
X= N = 5
= 13.6
To be a good measure of central tendency
the mean should be in the middle of the
scores…...
Median
The point in the distribution where 50% of
the scores lie above and 50% lie below
it.
The midpoint or 50th percentile
Position of the median
58
56
55
53
49
49
46
41
=N+1
2
4.5th score
=8+1
2
= 4.5th score
=9
2
Median lies between 53 and 49.
Average the two scores
53 + 49
2
= 51
Extreme scores do not greatly affect
the median
12
11
10
9
8
= median
30
11
10 = median
9
8
Mode
The score that occurs most frequently.
Rough measure for description more than
analysis purposes.
May be more than one….
Measures of variability:
Scatter or spread of scores from the
central tendency.
Tells us how heterogeneous or
homogeneous a group is.
Groups may have the same mean or
median but differ considerably in
variability.
Example:
Five students score 84, 80, 78, 75, 73 on
a test their mean is 78.
Another group of students scored: 98, 95,
78, 65, 54, their mean is also 78.
Obvious difference in variability of their
scores.
Range
Simplest measure or variability (weak).
Based on the two extreme scores.
Generally a large range = a large
variability.
Difference of the highest and lowest
scores in a data set.
Formula: high score - low score + 1
Standard Deviation
One of the best measures of variability.
Reflects the magnitude of the deviations
of the scores from the mean.
Mean (X) = X
N
Sd (s) = NX2 - (X)2
N(N - 1)
Variance:
The mean of the squared deviations from
the mean.
The standard deviation squared.
Computer as part of an ANOVA
procedure;
Often referred to as the mean square
(MS)
Normal Curve
99.73%
95.44%
68.26%
Sd
-3
-2
-1
0
1
2
3
z scores
-3
-2
-1
0
1
2
3
T scores
20
30
40
50
60
70
80
GRE,NTE
200
300
400
500
600
700
800
IQ Wechsler
55
70
85
100
115
130
145
Normal curve and comparative scores for various standardized
tests
Frequency Distributions:
1) Establish the range of scores from high
to low +1
2) Determine the size and number of step
intervals. (keep step intervals between
10 and 20)
Divide the range by 15
52/15 = 3.5 round up to 4 for intervals.
3) Set up the intervals;
The highest step must include the
highest score.
If the size of the step interval is an
even number, the lowest score in the
step interval should be a multiple of
the interval size.
If the size of the step is odd , the
middle score of the step interval
should be a multiple of the interval
size.
4) Tabulate the scores.
Provides the Researcher:
Info about the range
A rough indication of the measures of
central tendency
General manner in which the scores are
distributed.