Experiments And Statistics Flashcards
Experimentation begins by
formulating a number of research hypotheses.
Translate the different research hypotheses into a set of
treatment conditions and the selection of an appropriate experimental design within which to embody the different treatment conditions
Different treatments are administered to different groups of
subjects or to the same subjects in different orders and performance on some response measure is observed and recorded
Designing experiments
- Experimentation begins by formulating a number of research hypotheses.
- Translate the different research hypotheses into a set of treatment conditions and the selection of an appropriate experimental design within which to embody the different treatment conditions
- Different treatments are administered to different groups of subjects or to the same subjects in different orders and performance on some response measure is observed and recorded.
The treatment variable is commonly known as an
Independent variable
The measure is known as the
Dependent variable
An independent variable is the variable that is
Manipulated
Drug / Placebo
The dependent variable is the response measure which is
manipulated on the basis of the independent variables
Blood sugar levels
There are three kinds of independent variables:
- Quantitative variables are variables that represent variation in amount (e.g. amount of drug, loudness of noise).
- Qualitative variables represent variations in kind or type (e.g. teaching strategy).
- Classification variables systematically vary characteristics which are intrinsic to the subjects of the experiment (e.g. age, sex, IQ, species, word type, etc.)
Quantitative variables are variables that
represent variation in amount (e.g. amount of drug, loudness of noise).
A type of independent variable
Qualitative variables represent
variations in kind or type (e.g. teaching strategy).
A type of independent variable
Classification variables systematically vary
characteristics which are intrinsic to the subjects of the experiment (e.g. age, sex, IQ, species, word type, etc.)
Independent variable
Nuisance variables are potential
independent variables which if left uncontrolled could exert a systematic influence on the different treatment conditions.
Types of nuisance variables
- Several researchers running the same experiment might produce an experimenter effect.
- The time of day could have an influence.
- The kind of subject selected can effect the influence of the independent variables.
(Nusaince variable)
If we do not control for these differences in experimental situation…
we might have a confounding variable in the experiment
Once we have designed an experiment and have produced an experimental hypothesis then we need to decide upon
the specific details of the experiment.
The idea is to select a measure that will
capture” the hypothesised differences.
The measure that is adopted is known as the
Dependent variable
We hypothesise that the observed data will be somehow
dependent on the nature of the independent variable
Control in experimentation
- Consider an experiment where the data is collected by running the experiment simultaneously in two different laboratories:
- The two labs are identical in every respect except that the temperature for each room cannot be controlled.
- Temperature variations may lead to systematic variations in the performance on a task.
- Randomly allocating different treatment conditions to the rooms gives an equally likely “chance” that different random temperatures will be associated with the different treatment means.
Completely randomised designs
- The completely randomized design is characterized by the fact that the subjects are randomly assigned to serve in one of the treatment conditions.
- This is also known as a between subjects design since any differences in behaviour observed among the treatment conditions are based on differences between different groups of subjects.
Randomised block design uses
blocks of subjects who are matched closely on some relevant characteristic
- A common procedure is to treat a subject as a ‘block’, wherein the subject serves in all the treatment conditions of an independent variable.
- When subjects complete all the treatment conditions this type of design is commonly referred to as a repeated measures design or a within subjects design.
Statistical Hypothesises
5
- The Null Hypothesis
- The Alternative Hypothesis
- Deciding to Accept or Reject the Null Hypothesis.
- Errors in Hypothesis Testing.
- Juggling Type I and Type II Errors
A research hypothesis is a
fairly general statement about the assumed nature of the world that gets translated into an experiment.
Statistical hypotheses consist of a
set of precise hypotheses about the parameters of the different treatment populations.
Two statistical hypotheses are usually stated
- The Null Hypothesis
- The Alternative Hypothesis
- These are mutually exclusive or incompatible statements about the treatment parameters
The null hypothesis is the
statistical hypothesis which will be tested. It is often symbolized as Ho.
The function of the null hypothesis is to specify the
values of a particular population parameter (usually the mean) in the different treatment populations (symbolized as µ1, µ2, µ3 and so on).
The null hypothesis typically chosen gives the same
value to the different populations such that
•Ho: µ1=µ2=µ3=etc.
This is the same as saying that no treatment effects are present in the population
The alternative hypothesis
•If the parameter obtained from the treatment groups are too deviant from those specified by the null hypothesis, Ho, then the null hypothesis is reject in favour of the other statistical hypothesis, called the alternative hypothesis, H1.
Usually the alternative hypothesis states simply that
the different treatment populations are not all equal. Specifically,
•H1: not all µ’s are equal.
Deciding to reflect the null hypothesis or not
- A decision to reject Ho implies an acceptance of H1, which in essence, constitutes support of our original research hypothesis.
- On the other hand, if the parameter estimates are reasonably close to those specified by the null hypothesis, Ho is not rejected.
There is a problem with the way in which the null hypothesis and and alternative hypotheses are set up…
- For the null hypothesis
- All µ’s are equal
- For the alternative hypothesis
- All µ’s are not equal.
- These are statements at the level of the population means. However all we have are sample means.
We have to adopt a criteria for rejecting the null hypothesis…
- We do this by calculating test statistics based on the properties of the F-distribution.
- The value we adopt is called the significance level and is referred to as a (alpha).
- The value for a that we usually adopt in psychology is 0.05.
Errors in Hypothesis Testing
•The procedures we follow in hypothesis testing do not guarantee that a correct inference will be drawn.
•Whenever we make a decision about the Null Hypothesis we can make a mistake.
•There are two basic kinds of errors:
Type 1 error
Type 2 error
Type 1 Error
Reality •Null Hypothesis is true •Alternative Hypothesis is false Decision •Reject the Null Hypothesis •Accept the Alternative Hypothesis
Type 2 error
Reality •Null Hypothesis is false •Alternative Hypothesis is true Decision •Fail to reject the Null Hypothesis •Reject the Alternative Hypothesis
Juggling Type 1 and Type 2 errors
- Most of the time we do statistical analyses we are trying to juggle Type I and Type II errors.
- Generally, if it is important to discover new facts, then we may be willing to accept more Type I errors.
- On the other hand if it is important not to clog up the literature with false facts then we might be more willing to accept more Type II errors.
