L3 Flashcards
What are the 2 main features of a random binominal distribution?
- The outcomes are independent - random independent error variables
- They have a constant probability (coin flip has a constant probability of .5)
* But you need a large enough sample to generate this probability accurately*
What is the law of large numbers?
With many instances, chance evens out.
Events converge on their average probability.
What is the law of small numbers?
With few instances, chance is lumpy. In the short run, anything can happen.
The chance of getting all heads is much larger for
Larger or Smaller sample sizes?
Smaller
The bigger the sample size, the more accurately you can estimate the actual probability you are interested in.
What law is this?
Law of large numbers
What is the gamblers fallacy?
If something happens more frequently than normally in a short amount of time, the odds are that it should happen less frequently in the future (and vice versa)
What is the “regression to the mean”?
If a variable is extreme on its first measurement, it will tend to be closer to average on its second measurement
and if it is extreme on its second measurement, it will tend to have been closer to average on its first
It is a regression to mediocrity
Why should we be careful of jumping to causal conclusions when judging behaviour?
Regression to the mean and the law of large numbers mean that we need to be careful of attributing causal or systematic explanations for single observations
An increase or decrease in performance might simply be an example of regression to the mean
What are random independent variables?
Variables are independent if knowing the value of one of them does not change the probabilities for the other one
- Many things influence measurement besides the variable of interest.*
- These are nearly always independent of one another*
What is measurement error?
Regression is greatest with less precise measurement - where there is more variance
What are the two types of experiments in regards to participants?
Between-Subjects and Within-Subjects
Which experiment is “stronger”
Between-Subjects or Within-Subjects
Why?
Within Subjects
You can control for the random error that is introduced simply through the individuals differences when you assign people to different groups
What is a Between-Subjects design?
Different participants are assigned to different levels of the IV
- Participants are “nested” in the different conditions of your experiment*
- (e.g., treatment, placebo, or control)*
What is a Within-Subjects design?
The same participants are repeated in every level of your IV
Participants are ‘crossed’ with the different conditions of your experiment (e.g. fingerprints, faces and scrambled images)
Why is within-subject designs ideal in experimental designs?
Eliminates random error variance due to using different subjects in different conditions
Should you always try to manipulate IV in experimental designs?
Its almost always best to manipulate the independent variable if it is ethical to do so to remove randomness
What is a matched-pairs design?
You match participants on particular variables across key conditions in the experiments
- e.g. comparing experts of novices in a particular domain*
- They might be paired on age, or level of education or each pair of expert and novice. Each expert is paried with a novice and are compared across each condition. You match the pairs based on variables that might explain the outcome*
Why might you use a matched pairs design?
If you are not able to manipulate the IV of interest or do a within-subjects design
What is the advantage of using a matched pairs design?
Allows us to control for random error variance
Potential differences in the population that might explain the results
Potential disadvantages of Matched-Pairs Designs?
Might be difficult to find matched samples of participants (time consuming and resource intensive)
What is the pre-post design?
We are measuring something in different points of time and seeing if there is a difference between those measurements
When would we use a pre-post design?
When we don’t have complete control over the variable of interest
e.g. measuring participants knowledge before and after completing a course
What is the weakness of the pre-post design?
No control group
no comparison that we can say “it is because of the original reason that the results happened”
How do you account for the weakness of the pre-post design?
Have a control group or more than one control (important to have a placebo for example and a control which has no treatment)
What are the two best types of experiments for reducing random chance explanations?
Within-subjects design and if that is not possible paired-samples design.
Measuring differences
How might you measure the difference between two groups when running an experiment?
Comparing to a mean
How might you compare one mean to a theoretical number? (2 ways)
One sample t-test or one-sample wilcoxon rank sum test
What are the assumptions made in a one-sample t-test?
What are the assumptions of a one-sample wilcoxon rank sum test?
The observations are independent of one another
Lower power (higher Type 2 error rate)
What two types of analysis could we use to compare two means?
Independent samples t-test and Mann-Whitney U test
What are the assumptions of the independent samples t-test?
What are the assumptions of the Mann-Whitney U test?
- Independence: you need two independent, categorical groupos that represent your independent variable
- Continuous or ordinal scales
Why would you use a Mann-Whitney U test?
Makes less assumptions about the data
Assumption about the scale we are using is more relaxed (can be continuous or ordinal)
What analysis should you use for a matched-pairs design or a within subjects design when you want to compare two means?
Paired samples t-test or Wilcoxon signed rank test
What are the assumptions of a paired-samples t-test?
What are the assumptions of the Wilcoxon Signed Rank Test?
- Dependence: The independent variable consists of two categorical, ‘related groups’ or ‘matched pairs’.
2. Continuous or Ordinal scales
What does the normality assumption mean for paired samples t-tests?
the difference between the scores of the paired groups are normally distributed
Why would you use the Wilcoxon signed rank test?
It makes fewer assumptions than the paired samples t-test
What is the final alternative to the t-test / wilcoxon test?
Permutation test
What is a permutation test?
Resampling observed data without replacement many times in order to determine a p-value for our test
Assuming our distributional nature of our data (assuming normality) we are actually building or estimating our distribution by shuffling our data around
Describe the p-value in relation to the null hypothesis?
P-value: the probability of observing that data or more extreme when the null is true.
