STATISTICS
Lecture One: why do stats.
You can’t prove a hypothesis, but we can disprove a competing one. To prove a hypothesis to
be true, we would have to prove all conditions.
To disprove a hypothesis it only needs to be disproven once.
If two theories explain the data, we should select the simplest one.
Descriptive Statistics:
Graphical: bar charts, pie chart
Numerical: describe the average, range of the data
Inferential Statistics:
Testing for differences
Testing for correlations
Testing for interactions
Uses either analytic methods or brute force.
Variables = the things we measure – can take on many different values or categories
Continuous = can take on any value within a given data range. E.g. Temperature, Distance.
Discrete = only take on certain values within the range. E.g. reported number of symptoms of an
illness a person has / IQ scores.
Categorical = values are categories. E.g. Gender, occupation.
Researchers can convert continuous or discrete variables into categorical variables.
Experimental Design = manipulating one of the variables (IV) to see what effect is has on other
variables (DV). Also called true experiment.
Quasi-Experimental Design = If looking at males / females, you cannot randomly allocate people to
their groups.
Correlational Design = investigates the degree to which variables co-vary. But you can’t infer cause
and effect.
Repeated Measures / Within – participants: When one person does both conditions. Controls for
individual differences and needs fewer participants but people may become bored / familiar with
the experiment.
, Counterbalancing = reduces order effects. One half of the participants complete the first half of the
experiment followed by the second condition. The other half do the second condition then the first.
Independent Measures / Between - Participants = Different participants in each condition.
Requires more pps and no control over individual differences.
Matched – subjects design – like within.
Lecture Two: Hypothesis
Independent Variables – can have 2 or more levels.
Dependent Variables – what you measure.
Nominal – categorical, different classes, but not numerically related to each other. E.g. types of fruit,
ethnic background.
Ordinal – ranking, numbers indicate a relative position of something in a list, not equal intervals –
e.g. rank in a race.
Nuisance Variables – shouldn’t systematically bias results.
Experimental Hypothesis – what we think will happen in the experiment, aim of experiment.
Statistical Hypothesis – precise statements about the data.
Null hypothesis – the different samples come from same population – no difference.
Alternative Hypothesis – logical opposite of null hypothesis.
We reject the null hypothesis when the probability of the null hypothesis being true (p) is less
than some criterion.
Usually we set it at 0.05 (i.e. a one in 20 chance)
Lecture Three and Four: Descriptive and
Probability
Frequencies
Often the richest representations of your data are frequencies of occurrence.
Can represent as percentages too.
Cumulative Frequencies – people getting 5 or less, 10 or less...
Usually ordinal variables are discrete.
Interval / Ratio can be discrete or continuous.
Usually it isn’t sensible to calculate frequencies on the basis of every possible score – so we
create ranges or intervals of scores.
Lecture One: why do stats.
You can’t prove a hypothesis, but we can disprove a competing one. To prove a hypothesis to
be true, we would have to prove all conditions.
To disprove a hypothesis it only needs to be disproven once.
If two theories explain the data, we should select the simplest one.
Descriptive Statistics:
Graphical: bar charts, pie chart
Numerical: describe the average, range of the data
Inferential Statistics:
Testing for differences
Testing for correlations
Testing for interactions
Uses either analytic methods or brute force.
Variables = the things we measure – can take on many different values or categories
Continuous = can take on any value within a given data range. E.g. Temperature, Distance.
Discrete = only take on certain values within the range. E.g. reported number of symptoms of an
illness a person has / IQ scores.
Categorical = values are categories. E.g. Gender, occupation.
Researchers can convert continuous or discrete variables into categorical variables.
Experimental Design = manipulating one of the variables (IV) to see what effect is has on other
variables (DV). Also called true experiment.
Quasi-Experimental Design = If looking at males / females, you cannot randomly allocate people to
their groups.
Correlational Design = investigates the degree to which variables co-vary. But you can’t infer cause
and effect.
Repeated Measures / Within – participants: When one person does both conditions. Controls for
individual differences and needs fewer participants but people may become bored / familiar with
the experiment.
, Counterbalancing = reduces order effects. One half of the participants complete the first half of the
experiment followed by the second condition. The other half do the second condition then the first.
Independent Measures / Between - Participants = Different participants in each condition.
Requires more pps and no control over individual differences.
Matched – subjects design – like within.
Lecture Two: Hypothesis
Independent Variables – can have 2 or more levels.
Dependent Variables – what you measure.
Nominal – categorical, different classes, but not numerically related to each other. E.g. types of fruit,
ethnic background.
Ordinal – ranking, numbers indicate a relative position of something in a list, not equal intervals –
e.g. rank in a race.
Nuisance Variables – shouldn’t systematically bias results.
Experimental Hypothesis – what we think will happen in the experiment, aim of experiment.
Statistical Hypothesis – precise statements about the data.
Null hypothesis – the different samples come from same population – no difference.
Alternative Hypothesis – logical opposite of null hypothesis.
We reject the null hypothesis when the probability of the null hypothesis being true (p) is less
than some criterion.
Usually we set it at 0.05 (i.e. a one in 20 chance)
Lecture Three and Four: Descriptive and
Probability
Frequencies
Often the richest representations of your data are frequencies of occurrence.
Can represent as percentages too.
Cumulative Frequencies – people getting 5 or less, 10 or less...
Usually ordinal variables are discrete.
Interval / Ratio can be discrete or continuous.
Usually it isn’t sensible to calculate frequencies on the basis of every possible score – so we
create ranges or intervals of scores.
