PSYC 2030 Lecture Notes - Lecture 4: Standard Deviation, Normal Distribution
29 May 2018
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PSYC 2030 Lecture 4 Notes
Introduction
Significant Differences
• The computation assembles information about how much individual scores differ from
the mean.
• If your college or university attracts students of certain ability level, their intelligence
scores will have a relatively small standard deviation compared with the more diverse
community population outside your school.
• You can grasp the meaning of the standard deviation if you consider how scores tend to
be distributed in nature.
• Large numbers of data—heights, weights, intelligence scores, grades (though not
incomes)—often form a symmetrical, bell-shaped distribution.
• Most cases fall near the mean, and fewer cases fall near either extreme.
• This bell-shaped distribution is so typical that we call the curve it forms the normal
curve.
• A useful property of the normal curve is that roughly 68 percent of the cases fall within
one standard deviation on either side of the mean.
• About 95 percent of cases fall within two standard deviations.
• Thus, about 68 percent of people taking an intelligence test will score within ±15 points
of 100.
• About 95 percent will score within ±30 points.
• Data are noisy.
• The average score in one group (children who were breast-fed as babies, for example)
could conceivably differ from that in another group (children who were bottle-fed as
babies) not because of any real difference but merely because of chance fluctuations in
the people sampled.
• How confidently, then, can we infer that an observed difference is not just a fluke—a
chance result from the research sample?
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