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 X 50

10 X = N = 5 = 10

9

8

x1 50

What is happening here?

30

11 X 68

10 X = N = 5 = 13.6

9

8

X = 68

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 = N + 1

55 253 4.5th score

49 = 8 + 1 = 9

49 2 2

46

41 = 4.5th score

Median lies between 53 and 49.

Average the two scores

53 + 49

2 = 51

Extreme scores do not greatly affect the median

12 30

11 11

10 = median 10 = median

9 9

8 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) = NX2 - (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 Curve99.73%

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.