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4 Why can’t a hypothesis or theory ever be proven?

4 Why can’t a hypothesis or theory ever be proven?

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“Doing science”: hypotheses, experiments and disproof

(contraction) of land masses. This idea was quickly abandoned when the

theory of plate tectonics, which neatly explained variations in the direction

of the Earth’s magnetic field as recorded in the rock record as well as fossil

distributions across continents, was developed.

Another important historical example is the publication of Copernicus’

famous book in 1543, which presented evidence that the stars and planets

revolve around the Sun rather than the Earth. It took several decades of

discussion and the invention of the telescope to make the observations that

provided further support for this heliocentric perspective.


“Negative” outcomes

People are often quite disappointed if the outcome of an experiment is not

what they expected and their hypothesis is rejected. But there is nothing

wrong with this – rejection of a hypothesis is still progress in the process

of understanding how a system functions. Therefore, a “negative” outcome

that causes you to reject a cherished hypothesis is just as important as a

“positive” one that causes you to retain it.

Unfortunately researchers tend to be very possessive and protective of

their hypotheses, and there have been cases where results have been falsified

in order to allow a hypothesis to survive. This does not advance our understanding of the world and is likely to be detected when other scientists repeat

the experiments or do further experiments based on these false conclusions.

There will be more about this in a later chapter on ethics, which includes

discussion about doing science responsibly and ethically.


Null and alternate hypotheses

It is scientific convention that when you test a hypothesis you state it as two

hypotheses which are essentially alternates. For example, the hypothesis:

“Apatite treatment reduces the amount of lead leached from soil”

is usually stated in combination with:

“Apatite treatment does not reduce the amount of lead leached from soil.”

The latter includes all cases not covered by the first hypothesis (e.g. no

difference, or more lead in leachate from the apatite treatment).

2.7 Conclusion


These hypotheses are called the alternate and null hypotheses respectively. Importantly, the null hypothesis is always stated as the hypothesis of

“no difference” or “no effect.” So, looking at the two hypotheses above, the

second “does not” hypothesis is the null hypothesis and the first is the

alternate hypothesis. This is a tedious but very important convention

(because it clearly states the hypothesis and its alternative) and there will

be several reminders in this book.



There are five components to an experiment – (1) formulating a hypothesis,

(2) making a prediction from the hypothesis, (3) doing an experiment or

sampling to test the prediction, (4) analyzing the data, and (5) deciding

whether to retain or reject the hypothesis.

The description of scientific method given here is extremely simple and

basic and there has been an enormous amount of philosophical debate

about how science is done (see Box 2.1). For example, more than one

hypothesis might explain a set of observations and it may be difficult to

test these by progressively considering each one against its null. For further

reading, Chalmers (1999) gives a very clearly explained discussion of the

process and philosophy of scientific discovery.

Box 2.1 Two other views about scientific method

Popper’s hypothetico-deductive philosophy of scientific method, where

hypotheses are sequentially tested and always at risk of being rejected, is

widely accepted. In reality, however, scientists may do things a little


Kuhn (1970) argues that scientific enquiry does not necessarily proceed with the steady testing and survival or rejection of hypotheses.

Instead, hypotheses with some generality and which have survived initial

testing become well-established theories or “paradigms” which are relatively immune to rejection even if subsequent testing may find evidence

against them. A few negative results are used to refine the paradigm to

make it continue to fit all available evidence. It is only when the negative


“Doing science”: hypotheses, experiments and disproof

evidence becomes overwhelming that the paradigm is rejected and

replaced by a new one.

Lakatos (1978) also argues that a strict hypothetico-deductive process

of scientific enquiry does not necessarily occur. Instead, fields of enquiry,

called “research programmes” are based on a set of “core” theories that

are rarely questioned or tested. The core is surrounded by a protective

“belt” of theories and hypotheses that are tested. A successful research

program is one that accumulates more and more theories that have

survived testing within the belt, which provides increasing protection

for the core. If, however, many of the belt theories are rejected, doubt will

eventually be cast on the veracity of the core and of the research program

itself, which will be replaced by a more successful one.

These two views and the hypothetico-deductive view are not irreconcilable. In all cases observations and experiments provide evidence either

for or against a hypothesis or theory. In the hypothetico-deductive view

science proceeds by the orderly testing and survival or rejection of

individual hypotheses, while the other two views reflect the complexity

of theories required to describe a research area and emphasize that it

would be foolish to reject a theory outright on the basis of limited

negative evidence.



(1) Describe the “hypothetico-deductive” model of how science is done,

including the null and alternate hypotheses, the concepts of disproof

and the importance of a negative outcome.

(2) Why is it important to collect data from more than one sampling unit or

experimental unit when testing a hypothesis?


Collecting and displaying data



One way of generating hypotheses is to collect data and look for patterns.

Often, however, it is difficult to see any pattern from a set of data, which may

just be a list of numbers. Graphs and descriptive statistics are very useful for

summarizing and displaying data in ways that may reveal patterns. This

chapter describes the different types of data you are likely to encounter and

discusses ways of displaying them.


Variables, sampling units and types of data

In earth science applications, we usually consider three different types of data:

(1) Data organized in a sequence along a continuum of distance or time.

These data can be thought of as occurring in one dimension. For example,

you might be analyzing the composition or mineralogy of a drill core and

need to interpret spatial variation up and down the section.

(2) Data where sampling is done relative to some geographic or other type

of spatial context. These are usually two-dimensional data. Geologic

maps, contour diagrams, trend surface analyses and studies of spatial

relationships in thin sections all present opportunities to relate data to a

2-D system.

(3) Multivariate data in which the 1- or 2-D locations of the sampled data

are not relevant. Most types of chemical data fall into this category.

The particular attributes you measure when you collect data are called

variables (e.g. a chemical analysis, observations of humidity and air temperature, the thickness of some geological strata). These data are collected from

each sampling unit, which may be an individual (e.g. a single piece of rock)



Collecting and displaying data

or a defined item (e.g. a square meter of the outcrop, a specific stratigraphic

unit, or a particular locality).

If you only measure one variable per sampling unit the data set is univariate. Data for two variables per unit are bivariate, while data for three or

more variables measured on the same sampling unit are multivariate.

Variables can be measured on four scales – ratio, interval, ordinal or


A ratio scale describes a variable whose numerical values truly indicate

the quantity being measured.




There is a true zero point below which you cannot have any data

(for example, if you are measuring the length of feldspar crystals in a

thin section, you cannot have a crystal of negative length).

An increase of the same numerical amount indicates the same quantity

across the range of measurements (for example, a 0.2 mm and a 2 mm

feldspar will have grown by the same amount if they both increase in

length by 10 mm).

A particular ratio holds across the range of the variable (for example,

a 200 μm feldspar grain is twenty times longer than a 10 μm grain and a

100 μm grain is also twenty times longer than a 5 μm one).

An interval scale describes a variable that can be less than zero.




The zero point is arbitrary (for example, temperature measured in

degrees Celsius has a zero point at which water freezes), so negative

values are possible. The true zero point for temperature, where there is

a complete absence of heat, is zero kelvin (about –273 °C), so (unlike

Celsius) the kelvin is a ratio scale.

An increase of the same numerical amount indicates the same quantity

across the range of measurements (for example, a 2 °C increase indicates

the same increase in heat whatever the starting temperature).

Because the zero point is arbitrary, a particular ratio does not hold across

the range of the variable. For example, the ratio of 6 °C compared to 1 °C

is not the same as 60 °C to 10 °C. The two ratios in terms of the kelvin

scale are 279:274 K and 333:283 K.

An ordinal scale applies to data where values are ranked – which means

they are given a value that simply indicates their relative order. For

example, five mountains with elevations of 10 000 m, 4500 m, 4300 m,

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