Research Methods in Education
Dr. Olga Kritskaya
Topic:
Quantitative Research: Important Concepts and Terms
Operational Variable—
A variable that represents a characteristic (of interest to the researcher) of an
individual participant (or a group) as defined in terms of a specific measuring
instrument.
A Reflective Exercise: Defining Intelligence and Socioeconomic Status
Think about how you might assign numbers to the characteristics of intelligence
and socioeconomic status in order to conduct a quantitative study.
Administering a test is the obvious approach to quantify intelligence, but think
about how the test selected might affect the answer you would get about whether
there is a relationship between the two characteristics. For example:
- Would you be likely to come to a different conclusion about the
relationship if you used a nonverbal test?
- What kinds of things would you consider in assigning a numerical value
to socioeconomic status?
Mean— One of several measures of central tendency.
The average (M) that is a balance point in the distribution of scores obtained on a
variable. It is calculated by summing all the scores and dividing by the number of
scores (the latter usually represented the number of participants, n).
Median—One of several measures of central tendency.
The average (Mdn) that indicates the value below which half of the variable
scores (cases of measurement) lie (the variable scores are measured on a
particular measuring scale for each of the participating individuals/groups).
It is the point that divides a distribution of numerical values in half so that there
are the same number of values above this point as there are below it.
For example, if the median for a group of participants on a particular variable is
10.0, then 50% of the cases lie below 10.0.
Median – Examples:
- Eleven students took a midterm examination in a high school chemistry course and
received the following scores: 95, 90, 90, 89, 89, 87, 70, 64, 53, 45.
The median score is ....
- Only 10 students took the second examination in the course (one had dropped
the class); they received these scores: 93, 90, 90, 88, 86, 84, 84, 83, 82, 70.
The median scores in this case is ...
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Research Methods in Education
Dr. Olga Kritskaya
Mode—One of several measures of central tendency.
The mode is the most frequently occurring score (the category or numerical value
that occurs most often in a set of data).
For example, if more individuals receive a score of 29 than any other score, then
29 is the mode.
Mode – Examples:
- The scores of 18 students who took a 20-word spelling test are:
12, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 19, 19, 20.
The mode in this distribution of scores is … , because that is the score
received by the largest number of students.
- 40 people participating in a program at a senior citizen’s center were asked
which kind of fruits should be served at breakfast at the center. The number of
choices for each kind of fruit was recorded as follows:
Pears – 6
Grapes – 4
Strawberries – 5
Pineapples – 3
Oranges – 6
Apples – 9
All other fruit – 7
The category of … is the mode.
Variance –
This is a measure of the spread of scores (on a variable measure), that is, how far
they are spread out or dispersed.
Standard Deviation (SD) —A measure of variability.
It is statistics that shows the spread, or dispersion of scores in a distribution of
scores or other measurements. It is the most widely used and accepted measure of
variability. It tells how much, on the average, the values of a variable score in a
numerical distribution deviate from the mean. The more widely the scores are
spread out, the larger is the standardized deviation. The standard deviation (SD) is
calculated by taking a square root of the variance.
SD Examples:
- The students in two 10th grade classes took the same examination. In
the first class, the students’ scores on the test range from 70 to 86; in
the second, the scores range from 65 to 95. The standard deviation
would be larger for the scores of which class?
- The players on a boys’ basketball team and a men’s basketball team
stand side by side. The boys’ heights range from 4’6’’ to 5’9’’. The
men’s heights range from 6’0’’ to 6’7’’. The standard deviation in
height for the boys’ team, accordingly, is … that that of the men’s
team.
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Research Methods in Education
Dr. Olga Kritskaya
Chi-Square Test
The chi-square test is useful in relationships between categorical variables. It is
used to determine the likelihood (or probability) that an observed relationship
between two or more categorical variables is statistically significant (that is, not
due to chance alone).
As with all inference procedures, the chi-square test produces a value (χ2), which
can then be looked up in the appropriate table to see whether it is statistically
significant (see an example study in your textbook, Table 2, p. 181).
Observed frequency – In chi-square analysis, an actual count of the number of
objects in a particular category.
p-value
The small, italicized letter p in the term p value is short for probability value. It
is commonly in an expression such as p < .05. This expression means that the
probability (p) that a particular obtained result was due to chance is less than (<)
5% (.05). The smaller the p value, the greater is the likelihood that the obtained
result is not due simply to chance.
Validity
Validity refers to the degree to which evidence supports any inferences a
researcher makes based on the data he or she collects suing an instrument.
This idea is very important in selecting a measuring instrument.
Example:
Asking someone to tell what he or she knows about how to drive a car would not
usually be a valid way to find out whether the person actually can drive a car.
Reliability
The consistency of a measure or instrument from one use to another. A reliable
instrument is one that gives identical or very similar results in repeated
measurements of the same variable.
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