Transcript April 18

BHS 204-01
Methods in Behavioral
Sciences I
April 18, 2003
Chapter 4 (Ray) – Descriptive Statistics
Scales of Measurement

Nominal (categorical) – all-or-nothing
categorization or classification of responses.
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Example: religions, political parties, occupations
Ordinal – ordered by an underlying
continuum, degree of quantitative difference.
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Example: small, medium, large; child, teen, adult
Rank orderings: best, second best, worst
Scales of Measurement (Cont.)

Interval – ordered by a single underlying
quantitative dimension with equal intervals
between consecutive values.


Example: thermometer, rating scales
Ratio – an interval scale with an absolute zero
point.

Example: height, weight, yearly salary in dollars,
heart rate, reaction time to press a button.
Appropriate Statistics


Numbers do not know or care where they
came from (how you got them).
It is possible to apply any statistical test to
almost any set of numbers, but that doesn’t
make it right to do so.


Taking the average of football jersey numbers.
It is up to the experimenter to think about the
nature of the data when selecting statistics.
Frequency Distributions
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Data tells a story.
Techniques for analyzing data help you to
figure out what story your data is telling.
Frequency distribution – how frequently does
each score appear in your data set.


Bar graph
Frequency polygon (line graph)
Table 4.2. (p. 87)
Figure 4.1. (p. 88)
Bar graph of dream data.
Figure 4.2. (p. 88)
Frequency polygon of dream data.
Measures of Central Tendency

What single number best describes the data
set?
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Mean – arithmetical average of a set of scores.
Median – the middle score, so that half the
numbers are higher and half lower.
Mode – the most frequently occurring score.
Figure 4.4. (p. 91)
Mean, median, and mode
of (a) a normal
distribution and (b) a
skewed distribution.
Types of Frequency Distributions

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
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Normal – most scores are close to the mean.
Bimodal – the data set has two modes.
Positively skewed – extreme scores in the
positive direction
Negatively skewed – extreme scores in the
negative direction
In a skewed distribution, the mean is closest
to the direction of skew.
Figure 4.3. (p. 89)
Four types of frequency distributions: (a) normal, (b) bimodal, (c) positively
skewed, and (d) negatively skewed.
Measures of Variability

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Variability – how spread out are the scores.
Range – the distance between the highest and
lowest scores (largest score minus the
smallest scores).
Variance – the average of the squared
distances from the mean.

Sum of the squares divided by the number of
scores.
Figure 4.5. (p. 93)
Two different distributions with the same range and mean but different
dispersions of scores.
Standard Deviation


Average distance of scores from the mean.
Calculated by taking the square root of the
variance.


The variance scores were squared so that the
average of positive and negative distances from
the mean could be combined.
Taking the square root reverses this squaring and
gives us a number expressed in our original units
of measurement (instead of squared units).
Graphing Data

Line graph – used for ordinal, interval, ratio
data.

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Independent variable on the x-axis
Dependent variable on the y-axis
Bar graph – used for categorical data.
Figure 4.6. (p. 97)
Effects of room temperature on response rates in rats.
Figure 4.7. (p. 97)
Effects of different forms of therapy.
Transforming Data

Sometimes it is useful to change the form of
the data in some way:
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Converting F to C temperatures.
Converting inches to centimeters.
Transformation lets you compare results
across studies.
Transformation must preserve the meaning of
the data set and the relationships within it.
Standard Scores

One way to transform data in order to
compare two data sets is to express all scores
in terms of the distance from the mean.
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This is called a z-score.
z = (score – mean) / standard deviation
z-scores can be transformed so that all scores
are positive:
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This is called a T-score
T = 10 x z + 50
Measures of Association

Scatter plot – used to show how two
dependent variables vary in relation to each
other.
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One variable on x-axis, the other on y-axis.
Correlation – a statistics that describes the
relationship between two variables – how they
vary together.

Correlations range from -1 to 1.
Figure 4.9. (p. 102)
Scatter diagram showing
negative relationship
between two measures.
Figure 4.10. (p. 103)
Scatter diagrams showing various relationships that differ in degree and
direction.