Lecture notes

Lecture notes Statistical Methods Research Methods in Psychology – Evaluating a World of Information, ISBN: 9780393445213

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Module
Statistical Methods

Institution
The University Of Nottingham (UON)

Book
Research Methods in Psychology

Beth Morling Statistical methods notes.

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Uploaded on June 13, 2022
Number of pages 13
Written in 2021/2022
Type Lecture notes
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research
research methods
stats
statistics
statistical methods
statistical methods 1
beth morling
beth morling notes
lecture
lecture notes
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LECTURE 1

 Learning objectives – why and what to study in statistics
 The research process –

 Features of good scientific theories – supported by data; falsifiable; parsimony (Occam’s razor: all the other things being equal,
the simplest solution is the best); theories do not prove anything
 Daily life uses of statistics – understand what events were truly unlikely and what events were just chance
 Use of statistics in a job view – marketing; quality control; personnel; management; stock market; science
 Misuses of statistics – exaggerated graphics; revealing only part of the data; using hypothesis tests to make something sound
more important
 Importance of clarity – too many patterns; patterns change between graphs; too much data for one figure
 Descriptive statistics – graphical and numerical (average, range, etc.)
 Inferential statistics – testing for differences, correlations, interactions

LECTURE 2

 Learning objectives – scientific methods (experimental, quasi-experimental, correlational); variables (independent, dependent,
measurement scales); designs (between-subjects, within-subjects, matched-subjects); hypothesis (experimental, statistical)
 Experiment – vary some independent variable (IV) while holding everything else constant; measure changes in some
dependent variable (DV); changes in DV must have been caused by changes in IV (we can infer causality)
 Quasi-experiment – similar to experiment except IB cannot be manipulated; potential problems with confounding variables
 Correlational design – no manipulation; measure 2 (or more) variables and determine the extent to which they are related to
each other; cannot infer causality
 Independent variables can have 2 or more levels
 For example, test participants’ reading speed before a meal, immediately after and 2h after – 1 IV (time of day) with 3 levels
(before meal, after meal, 2h after meal)
 DV has several types or measurement scales – nominal, ordinal, interval, and ratio
 Nominal scale – numbers refer to different classes; classes not necessarily numerically related to each other
 Ordinal scale – numbers indicate a relative position in a list; rank is meaningful, items not necessarily at equal intervals
 Interval scale – equal steps are meaningful
 Ratio scale – equal steps are meaningful and there is a meaningful zero point
 Confounding variable – variable that confounds the interpretation of the results of an experiment; confounding occurs when
some aspect of the experimental situation varies systematically with the IV
 Between-subjects design – each condition is applied to a different group of participants; it is often the only option available;
individual differences (by assigning participants randomly to groups, individual differences should roughly balance between
groups)
 Within-subjects design – same participant performs at all levels of the independent variable; also known as repeated measures
design because participants repeat the measure for each different condition; this design is generally much more powerful
because each participant is their own control so individual differences are ruled out
 Withing-subjects design disadvantages – order effects; if all your participants do all conditions then make sure the order varies
either randomly or counterbalanced
 Matched-subjects design – researchers attempt to emulate some of the strengths of within subjects designs and between
subjects designs
 Correlational design – researcher seeks to understand what kind of relationships naturally occurring variables have with one
another
 Experimental hypothesis – questions that we wish to address in experiments, based on our theories
 Statistical hypothesis – precise statements about collected data
 The statistical hypothesis can be further divided into two types of hypothesis: null hypothesis and alternate hypothesis
 Null hypothesis – simple states that the different samples we look at come from the same population
 Alternative hypothesis – the logical opposite of the null hypothesis
 We reject the null hypothesis when the probability of null hypothesis being true (p) is less than some criterion (α)

,  Usually we set α=0.05 (i.e. a 1 in 20 chance)
 if p<0.05, we mean there was less than a 1 in 20 probability of it happening by chance
 To determine p, we calculate a test statistic
 The test statistic has known probabilities associated with its values
 p is the probability of collecting this data assuming the Null Hypothesis to be true
 i.e. the probability that the effect we measured is simply due to chance
 α (alpha) is the criterion level that we set: p has to be less than α for us to think the events we have measured are unusual.
 if p > α we have: “failed to reject the Null Hypothesis”
 this does not mean that it is true: just that we have not got any real reason to reject it (yet).

LECTURE 3

 Learning objectives – how we represent data in terms of frequency; the different measures of central tendencies; how we
represent data in terms of spread
 Categorical data – has two or more categories with no ordering to them; for example, hair colour, job title
 Discrete data (usually ordinal, ratio, or interval variables) – has fixed value with a logical order; for example, shoe size, score
out of 10
 Continuous data – can take any fractional value; for example, reaction times
 Categorical data – can be presented as its raw frequency or as a percentage frequency
 Measures of central tendency – sometimes we want to condense the entire frequency distribution to a single number; this is
where we might calculate the central tendency of the data
 Mode – the score occurring most often in a dataset; most common score; can be used for nominal data; sometimes takes more
than one value (bimodal and multimodal distributions)
 Median – the middle score in a dataset; the middle value in a dataset, or the mean of the middle two values; pros of median is
that its insensitive to outliers, often gives a real and meaningful data value, and useful for ordinal and skewed interval/ration
data; cons of median are ignores a lot of the data, difficult to calculate without a computer, and cannot use this with nominal
data
 Mean – sum of data points/number of data points; pros of mean are using all of the data and is most effective for normally
distributed datasets; cons of mean is that its sensitive to outliers, values are not always meaningful, and only meaningful for
ratio and interval data
 Mode – no measures of spread
 Median – ‘distance-based’ measures such as range and interquartile range
 Mean – ‘centre-based’ measures of spread such as variance and standard deviation
 Interquartile range – similar to range (highest score – lowest score) but ignores most extreme values; pros and cons are
identical to median
 Standard deviation is square root of variance
 Variance – pros are using all of the data and forms the basis of several other tests; cons are it requires a normal distribution,
sensitive to outliers, and units are not sensible
 Standard deviation – a measure of spread that is equal to the unit of measurement of the dependent variable; can measure
standard deviation of sample, population, or estimated standard deviation of a population based on a sample; allows us to get
an unbiased estimate of the population’s standard deviation if we only have access to a sample of data
 Sometimes you might want to use a frequency distributions and histograms to represent your data.
 Sometimes it is easier to use measures of central tendency and spread instead:
 Categorical data- use mode
 Ordinal data- use median and interquartile range
 Continuous data- use mean and standard deviation

LECTURE 4

 Learning objectives – what normal distribution is, and how this is associated with skew and standard deviations; how to
transform data using z scores; what sampling error is, how we might calculate it
 Normal distribution – when data is symmetrical around central scores; for example, flip a coin 20 times, repeat this thousands
of times; data should fit around a Gaussian curve

 Gaussian curve –

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Lecture notes

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