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To answer this question, researchers begin by stating a
null hypothesis , which predicts that the intervention or 100

treatment has no effect at all. In other words, any differ-
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ence between the test and control groups is due to chance 90
alone and nothing else is responsible for the difference
between the two groups. In this case, the null hypothesis is Average heart rate (beats per minute) 80 Average heart
that caffeine does not cause an increase in heart rate. They rate of students Error bar

also state an alternative hypothesis , which predicts that 70 after 0 cups
of coffee
the intervention or treatment has an effect, so the difference 60
between the test and control groups is real. In this case, the
alternative hypothesis is that caffeine causes an increase in 0 1 2 3 4
Cups of co ee
resting heart rate.
A statistical test normally yields a number, called the FIGURE 0.8 Error bars
p -value, that expresses the likelihood that an observed result An error bar represents a range of values within which the true value
could have been observed merely by chance. A p -value is a is likely to be. This graph shows the relationship between caffeine

,

probability. If p ≤ 0.05 (5%) there is less than or equal to a consumption and resting heart rate. It plots the average resting
5% chance that the observed results are the result of chance. heart rate of groups of people who consumed 0, 1, 2, 3, or 4 cups
of coffee, with error bars giving an indication of the uncertainty of
This is a relatively small chance. In this case, it is likely that the data.
the observed results in a dataset are real and not due to
chance. In other words, the null hypothesis is rejected. By As a result, you can think of the error bar as a way to show

,
contrast, if p > 0.05 there is greater than a 5% chance that the uncertainty of a measurement or data point.
the observed results could have been obtained by chance, so Throughout this course, you will have the opportunity
you fail to reject the null hypothesis. The phrasing “the null to learn some of the techniques researchers use to evaluate
hypothesis has failed to be rejected” reminds us that although data and to work with data yourself. “Tutorial 1: Statistics”
the results do not support the alternative hypothesis, it does on page 20 walks you through some of the statistics tools
not mean that the null hypothesis is correct. Rather, it sim- you will encounter. “Analyzing Statistics and Data: Averages”
ply means that the null hypothesis has not been disproven. gives you a chance to practice working with these concepts.
Finally, scientists are often interested in determining
how confident they should be in their data. Uncertainty can
be shown graphically as an error bar. An error bar is typically
®
PREP FOR THE AP EXAM
a short vertical line showing a range of values. For example, ®

FIGURE 0.8 shows results from our controlled experiment AP EXAM TIP
investigating the relationship between caffeine and resting When evaluating the results of an experiment, you should
heart rate. The data points indicate the average heart rate of be able to explain whether the alternative hypothesis is
the people in the groups. The vertical lines through the data supported or not, and whether the null hypothesis should
points are error bars. In spite of its name, an error bar doesn’t be rejected or fail to be rejected. you should know that
data are often analyzed statistically to determine if real
represent an error or a mistake. Instead, it shows a range of differences exist between the data collected from the
values that incorporates small differences among the indi- experimental and control groups.
viduals and perhaps even inaccuracies in the measurements.

MODULE 0 IntroductIon 11

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