Variables
Independent variable – a variable the experimenter has manipulated, thought to be
the cause of some effect
Dependent variable – the variable that is measured (an outcome). Affected by
changes in IV
Predictor variable – variable thought to predict outcome variable. Another way of
saying IV.
Outcome variable – thought to change as a function of changes in a predictor
variable. Aka DV.
Levels of measurement
Categorical (entities are divided into distinct categories
o Binary variable – only two categories (dead or alive)
o Nominal variables – more than two categories (whether someone is
omnivore, vegetarian vegan etc)
o Ordinal variable – same as nominal but this has a distinct order (whether
someone got a fail, pass, merit or distinction in exam)
Continuous (entities get a distinct score)
o Interval variable – equal intervals on variable represent equal differences in
property being measured (e.g. differences bet. 6 and 8 is equal to differences
bet. 13 and 15)
o Ratio variable – same as interval, but ratio of scores on scale must also make
sense (e.g. score of 16 on an anxiety scale means the person is twice as
anxious as someone scoring 8). The scale must have a meaningful zero point
for this to be true.
Central tendency
Mean = sum of all scores divided by number of scores. Can be influenced by extreme
scores.
Median – middle score, when placed in ascending order. Not influenced by extreme
scores
Mode – score that occurs most frequently
Dispersion
Deviance/error is distance of each score from mean
Sum of squared errors – total amount of error in the mean. Errors/deviances are
squared before adding them up.
Variance – av. distance of scores from mean. The sum of squares divided by number
of scores. Tells us how widely dispersed scores are around the mean.
Standard deviation – square root of variance. The variance converted back to the
original units of measurement of the scores used to compute it. Large sds relative to
mean suggest data are widely spread around mean, whereas small sds suggest data
= closely packed around mean.
Range – distance between highest and lowest score
, Interquartile range – range of the middle 50% of scores
Distributions and z-scores
Frequency distribution – a table or chart showing each possible score on a scale of
measurement along with the number of times that score occurred in the data.
Scores are sometimes expressed in a standard form known as z-scores
To transform a score into a z score you subtract from it the mean of all scores and
divide the result by the sd of all scores
The sign of the z-score tells us whether the original score was above or below the
mean; the value of the z score tells us how far the score was from the mean in sd
units.
Chapter 2
The standard error
It is the standard deviation of sample means. A measure of how representative of
the population a sample mean is likely to be.
A large standard error (relative to sample mean) means there’s a lot of variability
between the means of different samples and so the sample mean we have might not
be representative of the population mean.
A small SE indicates that most sample means are similar to the population mean (i.e.
our sample mean is likely to accurately reflect the population mean)
Confidence intervals
Confidence interval for the mean is a range of scores constructed such that the
population mean will fall within this range in 95% of samples.
Confidence interval is not an interval within which we are 95% confident that the
population mean will fall.
Null hypothesis significance testing (NHST)
It’s a widespread method for assessing scientific theories. The basic idea that we
have two competing hypotheses; one says an effect exists (alternative hyp.) the
other says an effect doesn’t exist (null hyp.).
We compute a test statistic that represents the alternative hypothesis and calculates
the probability that we would get a value as big as the one we have if the null
hypothesis were true.
If probability is less than .05 we reject idea that there is no effect,(reject the null
hypothesis) say that we have a statistically significant finding.
If probability is more than .05 we do not reject the idea that there is no effect (don’t
reject null hyp.), we say that we have a non-significant finding.
We can make two types of error: we can believe that there is an effect when there
isn’t (type I error) and we can believe there’s not an effect when there is (type II
error)
Power of a statistical test is probability that it will find an effect when one exists
Significance of a test statistic is directly linked to the sample size; the same effect will
have different p-values in different sized sample, small differences can be deemed
‘significant’ in large samples and large effects might be deemed ‘non-significant’ in
small samples.
Chapter 3
, Problems with NHST
Poorly understood things related to significance testing:
o A significant effect is not necessarily an important one
o A non significant result does not mean that the null hypothesis is true
o As significant result does not mean that the null hypothesis is false
NHST encourages all or nothing thinking whereby an effect with a p value just
below.05 is perceived as important whereas one with a p value just above.05 is
perceived as unimportant
NHST is biased by researchers deviating from their initial sampling frame (e.g.
stopping data collection earlier than planned)
Lots of ways scientists can influence p value. AKA researcher degrees of freedom and
include
o Selective exclusion of data
o Fitting different statistical models but reporting only one with the most
favourable results
o Stopping data collection at a point other than that decided at the study’s
conception
o Including only control variables that influence the p value
Incentive structures in science that reward publication of significant results als
reward the use of researcher degrees of freedom
P-hacking – refers to practises that lead to the selective reporting of significant p
values, most commonly trying multiple analyses and reporting only the one that
yields significant results.
Hypothesizing after the results are known (HARKing) occurs when scientists present
a hyp that was made after data analysis as though it were made at the study’s
conception.
Effect sizes and meta analysis
Effect size – way of measuring the size of an observed effect, usually relative to the
background error
Cohen’s d – the difference bet two means divided by the SD of the mean of the
control group, or by a pooled estimate based on the SD of both groups.
Pearson’s correlation coefficient (r) – is a versatile effect size measure that can
quantify strength and direction of relationship bet two continuous variables, also
quantifies the difference bet groups along a continuous variable. Ranges from -1
(perfect negative relationship) through 0 (no relationship at all) to +1 (a perfect
positive relationship)
The odds ratio is the ratio of the odds of an event occurring in one category
compared to another. An odds ratio of 1 indicates that the odds of a particular
outcome are equal in both categories
Estimating the size of an effect in the population by combining effect sizes from
different studies that test the same hypothesis is called meta analysis
Summary of Bayesian process
1) Define a prior that represents your subjective beliefs about a hypothesis (the prior is
a single value) or a parameter (the prior is a distribution of possibilities). The prior
can range from uninformative (prepared to believe pretty much anything) to strongly
informative ( your initial beliefs are quite narrow and specific).
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