variables

central tendency

variability

correlation

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A variable is simply something that "varies" or doesn't always have the same value.

In psychological measurement, variables are typically classified into one of three levels:

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A CATEGORY VARIABLE is one in which changes occur in all-or-none steps. It is digital.

Your social security number is a nominal or category variable.

Examples of category variables include:

whether a student is present or absent

whether a student's performance is classified as mastery or non-mastery.

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A RANKED VARIABLE does not have the precision of equal units.

Measurement with ranked variables simply put things in order, for example from highest to lowest.

An example is the measurement of academic achievement with a grade equivalent score or a percentile rank.

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A CONTINUOUS VARIABLE has "continuous" gradations of magnitude which are equal units.

It is analogue (like an old fashioned clock with a moving second hand).

Examples would include the measurement of height, weight, academic aptitude with a standard score scale, and so forth.

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I measured the lines below and assigned the number at the end of the line.

______ 3

_____________________________ 1

___________________________ 2

This measurement is at which level:

a. nominal (category)

b. ordinal (rank)

c. interval (continuous)

CENTRAL TENDENCY describes the clustering of values (for example, test scores) around some more or less central value.

The MEAN is the sum of the scores divided by the number of scores.

The MEDIAN is the point above and below which are 50% of the scores.

The MODE is the score occurring most frequently.

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When determining CENTRAL TENDENCY, remember that use of the "mean" as the measure of central tendency should usually be your first consideration. It is the only measure of central tendency which can be weighted and manipulated algebraically. But, the mean can be misleading if there are extreme scores (scores which are significantly higher or lower than the majority of the other scores).

The median is less affected by extremes.

The mode is the least stable, but it is the only measure of central tendency appropriate if the measurement is at category (nominal) level.

You calculate the MEAN just as you learned to find the arithmetic average (total of scores divided by number of scores)

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To calculate the MEDIAN, first put the scores in rank order (highest to lowest or lowest to highest). Then, if there are an odd number of scores count down to the middle score. The value of that score is the median. For example, if there are fifteen scores, the median would be the value of the eighth score from top or bottom. There would be seven scores above and seven scores below.

If there are an even number of scores, divide the number of scores by two. Then count down to that quotient; add the value of that score to the value of the next score. Divide by two. That answer is the median.

For example, if you had these scores: 10, 9, 8, 7, 6, 6, 5, 1

In the example, there are an even number of scores (8). Divide 8 by 2; the quotient is four. The fourth score down is a 7. The next score is a 6. Add 6 to 7, divide the answer by 2 (13/2). The median is 6.5.

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In the following distribution, what is the median?

17 10 15 14 11 12 13

a. 13

b. 14

In the following distribution, what is the median?

27 25 16 24 25 16 16 21 23 22

a. 23

b. 22.5

c. 22

YOU ARE CORRECT.
The measurement level would be classified as ordinal (rank) because the units of measurement are not equal. The length of lines 1 and 2 is nearly the same while there is a large gap between the length of line 2 and line 3.

______ 3

_____________________________ 1

___________________________ 2

_____________________________________________________________________

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No, the measurement level would be classified as ordinal (rank) because the units of measurement are not equal. The length of lines 1 and 2 is nearly the same while there is a large gap between the length of line 2 and line 3.

______ 3

_____________________________ 1

___________________________ 2

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YOU ARE CORRECT.

The median is 13.

The scores were: 17 10 15 14 11 12 13

First step is to put them in rank order: 17 15 14 13 12 11 10

There are an odd number of scores (7).

Counting down to the middle score (4th from top or bottom), the median is 13.

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No, the median is 13.

The scores were: 17 10 15 14 11 12 13

First step is to put them in rank order: 17 15 14 13 12 11 10

There are an odd number of scores (7).

Counting down to the middle score (4th from top or bottom), the median is 13.

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YOU ARE CORRECT.

The scores were: 27 25 16 24 25 16 16 21 23 22

First step is to put them in rank order: 27 25 25 24 23 22 21 16 16 16

There are an even number of scores (10).

Dividing 10 by 2, you then count down to that quotient (fifth score). Add the fifth to the sixth (23 + 22) and divide the answer by 2.

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No, the median is 22.5.

The scores were: 27 25 16 24 25 16 16 21 23 22

First step is to put them in rank order: 27 25 25 24 23 22 21 16 16 16

There are an even number of scores (10).

Dividing 10 by 2, you then count down to that quotient (fifth score). Add the fifth to the sixth (23 + 22) and divide the answer by 2.

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