This is a summary of the book Discovering Statistics Using IBM SPSS Statistics by Andy Field (5th edition). Chapters 1, 2, 4-6, 8-10, 12, 14, 18 and 19 are included. The summary is in English, with a few dutch clarifications/translations.
Exam Guide for Applied Multivariate Data Analysis – Get yourself a Wonderful Grade!
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Statistics summary
Discovering Statistics - chapter 1
1.2. What the hell am I doing here? I don’t belong here
When numbers are involved, the research involves quantitative methods, but you can also generate and test
theories by analysing language. This involves qualitative methods.
1.3. The research processes
The research process starts with an observation that you want to understand. From your initial observation
you consult relevant theories and generate explanations (hypotheses) for those observations, from which you
can make predictions. To test these predictions, you need data. First you collect data and then you analyse it.
The result can be that the data support your hypothesis or not.
1.5. Generating and testing theories and hypotheses
A hypothesis is a proposed explanation for a fairly narrow phenomenon or set of observations. It is not a guess,
but an informed, theory-driven attempt to explain what has been observed. Theories and hypotheses exist in
the conceptual domain, and you cannot observe them directly. To test this hypothesis, we need to move from
the conceptual domain into the observable domain. We do this by using predictions. Predictions emerge from
a hypothesis and transform it from something unobservable into something that is.
Scientific statements can be confirmed or disconfirmed empirically. It must be testable. A statement that can’t
be proved or disproved is called a non-scientific statement. Non-scientific statements can sometimes be
altered to become scientific statements.
Fester Ingpant-Stain’s theory explains the initial observations and brings together a range of research findings.
The end result of this whole process is that we should be able to make a general statement about the state of
the world.
Falsification is the act of disproving a hypothesis or theory.
1.6. Collecting data: measurement
1.6.1.
To test hypotheses, we need to measure variables. Variables are things that can change or vary. Most
hypotheses can be expressed in terms of two variables: a proposed cause and a proposed outcome. The key
to testing scientific statements is to measure the variables.
• Independent variable: A variable thought to be the cause of some effect. This term is usually used in
experimental research to describe a variable that the experimenter has manipulated. This is the one
that is changed or controlled in an experiment, to test the dependent variable.
• Dependent variable: A variable thought to be affected by changes in an independent variable. You can
think of this variable as an outcome. This is the one being tested.
• Predictor variable: A variable thought to predict an outcome variable. This term is basically another
way of saying ‘independent variable’.
• Outcome variable: A variable thought to change as a function of changes in a predictor variable. For
the sake of an easy life this term could be synonymous with ‘dependent variable’.
,Researchers can’t always manipulate variables. Instead they sometimes use correlational methods. for which
it doesn’t make sense to talk of dependent and independent variables because all variables are essentially
dependent variables.
1.6.2.
The relationship between what is being measured and the numbers that represent what is being measured is
known as the level of measurement. Variables can be categorical or continuous.
Variables can be split into categorical and continuous, and within these types there are different levels of
measurement:
• Categorical (entities are divided into distinct categories):
o Binary variable: There are only two categories (e.g., dead, or alive).
o Nominal variable: There are more than two categories (e.g., whether someone is an omnivore,
vegetarian, vegan, or fruitarian).
o Ordinal variable: The same as a nominal variable but the categories have a logical order (e.g.,
whether people got a fail, a pass, a merit, or a distinction in their exam).
• Continuous (entities get a distinct score):
o Interval variable: Equal intervals on the variable represent equal differences in the property
being measured (e.g., the difference between 6 and 8 is equivalent to the difference between
13 and 15).
o Ratio variable: The same as an interval variable, but the ratios of scores on the scale must also
make sense (e.g., a score of 16 on an anxiety scale means that the person is, in reality, twice
as anxious as someone scoring 8). For this to be true, the scale must have a meaningful zero
point.
Continuous variables can be continuous and discrete. Continuous variables can be measured to any level of
precision (infinitive level of precision). A discrete variable can take on only certain values on the scale, the
actual values that the variable takes on are limited. (For example, by a 1-5 scale you can’t choose 4.28).
1.6.3.
The distinction between continuous and discrete variables can be blurred. For one thing, continuous variables
can be measured in discrete terms; for example, when we measure age, we rarely use nanoseconds but use
years (or possibly years and months).
There will often be a discrepancy between the numbers we use to represent the thing we’re measuring and
the actual value of the thing we’re measuring discrepancy is known as measurement error. Self-report
measures will produce larger measurement error because factors other than the one you’re trying to measure
will influence how people respond to our measures.
1.6.4.
One way to try to ensure that measurement error is kept tot a minimum is to determine properties of the
measure that give us confidence that it is doing its job properly. The first property is validity, which is whether
an instrument measures what it was designed to measure. The second is reliability, which is the ability of the
measure to produce the same results under the same conditions.
When data are recorded simultaneously using the new instrument and existing criteria, then this is said to
assess concurrent validity; when data from the new instrument are used to predict observations at a later
point in time, this is said to assess predictive validity. Assessing criterion validity is often impractical because
,objective criteria that can be measured easily may not exist. we can also assess the degree to which individual
items represent the construct being measured and cover the full range of the construct (content validity).
The easiest way to assess reliability is to test the same group of people twice: a reliable instrument will produce
similar scores at both points in time (test–retest reliability).
1.7. Collecting data: research design
In correlational or cross-sectional research, we observe what naturally goes on in the world without directly
interfering with it, whereas in experimental research we manipulate one variable to see its effect on another.
1.7.1.
In correlational research we observe natural events; we can do this by either taking a snapshot of many
variables at a single point in time, or by measuring variables repeatedly at different time points (known as
longitudinal research). This provides a neutral view because nothing will be influenced. That is an important
aspect of ecological validity. Correlational research tells us nothing about the causal influence of variables.
1.7.2.
Most research questions can be broken down into a proposed cause and a proposed outcome. Both the cause
and the outcome are variables. The key to answering the research question is to uncover how the proposed
cause and the proposed outcome relate to each other. David Hume, an influential philosopher, defined a cause
as ‘An object precedent and contiguous to another, and where all the objects resembling the former are placed
in like relations of precedency and contiguity to those objects that resemble the latter’.
In correlational research variables are often measured simultaneously. A limitation of correlational research
is the tertium quid. Confounding variables are extraneous factors that you were not considered but influences
the outcome. Experimental methods strive to provide a comparison of situations (usually called treatments or
conditions) in which the proposed cause is present or absent.
1.7.3.
There are two ways to manipulate the independent variable. First is to test different entities (=eenheid)
(between-groups, between-subject or independent design). An alternative is to manipulate the independent
variable using the same entities (within-subject or repeated-measures design). The way in which the data are
collected determines the type of test that is used to analyse data.
1.7.4.
A small difference in performance created by unknown factors is called unsystematic variation. Differences in
performance created by a specific experimental manipulation are known as systematic variation. In
conclusion:
• Systematic variation: This variation is due to the experimenter doing something in one condition but
not in the other condition.
• Unsystematic variation: This variation results from random factors that exist between the
experimental conditions (such as natural differences in ability, the time of day, etc.).
In a repeated-measures design, differences between two conditions can be caused by only two things: (1) the
manipulation that was carried out on the participants, or (2) any other factor that might affect the way in
which an entity performs from one time to the next. In an independent design, differences between the two
conditions can also be caused by one of two things: (1) the manipulation that was carried out on the
participants, or (2) differences between the characteristics of the entities allocated to each of the groups.
, 1.7.5.
It is important to try to keep the unsystematic variation to a minimum. Then we get a more sensitive measure
of the experimental manipulation. Scientist use randomization of entities to treatment conditions to achieve
this goal. Randomization is important because is eliminates the most other sources of systematic variation.
We can use randomization is two different ways depending on whether we have an independent or repeated-
measures design.
The two most important sources of systematic variation in this type of design are:
• Practice effects: Participants may perform differently in the second condition because of familiarity
with the experimental situation and/or the measures being used.
• Boredom effects: Participants may perform differently in the second condition because they are tired
or bored from having completed the first condition.
These effects are impossible to eliminate completely, we can ensure that they produce no systematic variation
between our conditions by counterbalancing the order in which a person participates in a condition. We can
use randomization to determine in which order the conditions are completed. That is, we randomly determine
whether a participant completes condition 1 before 2 or 2 before 1.
1.8. Analysing data
1.8.1.
Plot a graph of how many times each score occurs is known as a frequency distribution or histogram. These
can be useful for assessing properties of the distributions of scores. There are different types of frequency
distributions. The first is the normal distribution (bell-shaped). But there are two main ways in which a
distribution can deviate from normal: (1) lack of symmetry (called skew) and (2) pointiness (called kurtosis).
Skew can be positive (more at left side) and negative (more at right side). A positive kurtosis is called heavy-
tailed distribution or leptokurtic (very pointy). A negative kurtosis is thin in the tails and is called platykurtic.
In a normal distribution the values of skew and kurtosis are 0. If a distribution has values of skew or kurtosis
above or below 0 then this indicates a deviation from normal.
1.8.2. / 1.8.3. / 1.8.4.
The centre of a frequency distribution is known as the central tendency. Therefore, three measures are
commonly used: mean, mode and median.
• The mode is the score that occurs most frequently (one problem, it can have more than two). With
two it is called bimodal and with more than two multimodal.
• The median is the middle score when the scores are placed in ascending order. It is not as influenced
by extreme scores as the mean. You can calculate the location of it: (n+1)/2. It works nice when there
is an odd number of scores.
• The mean is the sum of all scores divided by the number of scores. The value of the mean can be
∑𝑛
𝑖=1 𝑥𝑖
influenced quite heavily by extreme scores. This formula is as follows: 𝑥̄ = n
. Be careful with
outliers.
1.8.5.
The easiest way to look at dispersion is to take the largest score and subtract from it the smallest score. This
is known as the range of scores. When there are extreme scores you can solve this problem by calculating the
range but excluding values at the extremes of the distribution. One convention is to cut off the top and bottom
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