Part F: A Closer Look at....
(or How to tell the truth with statistics)
A First Look
People who do science ask questions. Which causes produce which effects? How are
phenomena related? How can we usefully describe what we observe? Although particular
quantitative details of the relationships are also important, these are rarely the first stage of a
scientific investigation. erving the Effects of Solar Ultraviolet Radiation on
Yeast,showed unequivocally that exposure to sunlight damages a certain strain of yeast. No
statistical evidence is needed to establish the effect, but lots of further investigation is suggested:
could it be the rise in temperature that damages the cells? Would an incandescent light bulb hurt
them in the same way? Why does a transparent glass plate protect the cells? Following up these
leads, and others that occur to you is real science, and it is science without statistics. Pursuit of
question and answer, which should be the basis for science education, is accessible even to young
students for whom "mean," and "standard deviation," and "confidence level," would be merely
We've heard some science educators assume that if a statement is not quantified then it is
not scientific, that only sentences like "The probability of 0.95 that ..." are scientific. Such a view
can damage science education because it divorces thinking about science from all the rest of our
thinking about the world. Scientific thinking is ordinary logic, ordinary reasoning, ordinary
thinking; an answer is scientific if it can be tested by ordinary people.
Consider the questions raised by the experiment on the dose dependence of survival rates.
Earlier experiments establish that UV radiation affects yeast cells, and now the question is how
the dose affects damage. The first response should be qualitative, phrased in ordinary language,
rather than with numbers or equations: the larger the dose of UV, the lower the surviving fraction
of cells. This rough relationship is not foreordained and is the first important result of this
experiment. Even young students can discuss this observation in scientific, qualitative terms.
Slightly more advanced students may use the statistical ideas of "average" and "standard
deviation" to present data simply and think more specifically about the results.
In thinking about how to design and run classroom experiments some statistical thinking is
called for. For example, you need to estimate how many cells are going to survive each dose of
UV so that you use reasonable dilution factors. It is useful also to have a little knowledge of a
"normal distribution," mainly just that about 1/3 of the data points will typically lie outside one
standard deviation from the mean, about 1/20 will lie outside two standard deviations, and less
than 3/100 will lie more than three standard deviations from the mean. This allows you to
disregard points more than 3 or 4 standard deviations from the mean with some confidence. (But
you ought to also be sensitive to the possibility that the kid with the wild plate may have run into
something interesting.) Finally, to appreciate the power of having lots of data. The larger your
sample size, the smaller your relative error bars get and the more clear-cut your results become.
A Second Look
Students of science try to find out what is happening, describe it usefully, and, in some sense,
understand what is going on. What is happening in the experiments in this unit of study? We find
that exposure to UV light damages some strains of yeast so that they can't reproduce, that this
exposure can cause mutations, and that exposure to sunlight can induce some repair of the
damage. We are doing the experiments to try to understand these phenomena better, in some
cases even in a quantitative way. Although we are not testing any hypothesis, we may form one
during our investigation. The statistical language of hypothesis testing is unnecessary for
describing the experiments and their results. When we talk of "statistics" we usually refer only to
concepts such as "average," "experimental error," or "standard deviation." Terms like
"confidence levels," "t-tests," and even "chi-square" are rarely needed. When you do use
statistical concepts, don't turn them into hard-and-fast rules. For "error," you may sometimes use
the whole range of results from a class, or instead of reporting the "average," you may record the
We could recast our experiments as hypothesis testing. Instead of measuring the surviving
fraction of cells vs. dose, for example, we could try to discredit the hypothesis that the log of the
surviving fraction varies linearly with exposure time. Such an approach would make all the
statistics learned in ed psych classes applicable. Wouldn't this be a good thing? No. First, it
would distort what scientists really do, namely, try to figure stuff out, to discover rather than
hypothesize. Second, it would require talking and thinking about science in a different way than
we use in the rest of our lives, and this would be misleading: science uses ordinary logic and
ordinary speech, it is not something esoteric reserved to a priesthood of the elect. Third, framing
the work as hypothesis testing would be harder. Asking "what's going on?" is easier than asking
"what is the probability that the data are inconsistent with the hypothesis?". And finally,
hypothesis testing closes off other questions that the more open-ended "what's happening?"
Having thoroughly discredited the use of sophisticated statistics in experiments, let's soften
the stance a bit. Sometimes we ARE "hypothesis testing." In the photoreactivation experiment,
for example, one (but only one) of the questions we should ask is "Is there any difference between
the cells exposed to sunlight and those kept in the dark?" Here a chi-square test or a t-test would
be appropriate although unnecessary (if the experiment was well-designed.) You might also use a
chi-square to compare data to an existing theory such as Mendelian genetics. Chi-square will
enable you to quantitatively compare segregation ratios obtained in crosses with the ratios
predicted by a genetic model (e.g. unlinked genes).
If we can use chi-square to evaluate how well a given curve fits a set of data, we could use
the data both to obtain the curve and to evaluate how good the fit is. Students at preparatory
levels, however, would struggle to do this properly. They would find it especially hard to handle
the effect of points with differing errors and decide on the right number of "degrees of
There is no prescription for doing science, no infallible list of rules. Teach your students
to use common sense, think hard and be honest. Encourage them to behave like scientists,
beginning their work by finding out what happens and describing it in everyday language. As their
knowledge builds, you may begin to incorporate quantitative elements. Use this process as a
1. Observe effects and investigate causes.
2. Describe relationships qualitatively.
3. Plot all results on graphs. Experiment with linear, log-linear, and log-log graphs.
4. Make graphs of averages (or other estimates) using standard deviations (or another
measure of error) as error bars.
5. Look for the "best fit" between a simple curve (often a straight line on some graph) and
the data. First, by eye; then, perhaps, using "least squares."
6. If a theory exists and specifies parameters for the curve in #5, then you may try to
determine a "confidence interval" for some of the parameters. Remind your students that
scientists rarely determine "confidence intervals." Glance through Physical
Review or Genetics to see how many error bars and how few confidence levels there
A Last Note
We think the urge to quantify all scientific questions and answers arises from the
knowledge that science is partly institutionalized doubt, that we are never absolutely sure about
anything, and that therefore it is wonderful that we can go so far when we are always beset by
uncertainty. Science students can benefit enormously when this philosophy becomes central to
the classroom, because it stimulates questioning. But if we suggest to students that this
uncertainty means that we don't really learn anything with all our work, or that we have to talk
and think differently about the natural world than about anything else, then this preoccupation
with quantifying our uncertainty becomes a barrier to science education.
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Last updated Friday July 11 1997