20. Correlations & Distributions Flashcards
What is correlation
- Correlation is a measure of the relationship between 2 variables
(eg it can tell you how closely exam grades are related to the amount of revision done). - In a correlational study, data is collected for some kind of correlational analysis.
What is the Correlation Coefficient
A number between -1 and +1
How does the Correlation Coefficient work
- First, collect some data. You can then work out a correlation coefficient. (One statistical test that calculates a correlation coefficient is the Spearman’s rho test).
What does the Correlation Coefficient show
- How closely the variables are linked. This is shown by the size of the number - it its close to +1 or -1, then they are very closely related, while a smaller number means the relationship is less strong (or maybe not there at all if its close to 0).
- The type of relationship - a positive correlation coefficient (between 0 and +1) means that the variables rise & fall tg, while a negative correlation coefficient (between -1 and 0) means that as one variable rises, the other falls.
Where can correlations be viewed
On scattergrams
see pg117 for egs
What does a Positive correlation mean
As one variable rises, so does the other.
Correlation coefficient is roughly 0.75 (close to +1).
What does a Negative correlation mean
As one variable rises, the other one falls (and vice versa).
Correlation coefficient is roughly -0.75 (close to -1).
What does a Zero correlation mean
If the correlation coefficient is 0 (or close to 0), then the two variables arent linked.
ADVANTAGES of Correlational research
- Bc correlational research doesnt involve controlling any variables, it can be done when a controlled experiment cannot be conducted (for practical or ethical reasons).
- For eg, an experiment into the effects of smoking on humans probably wouldn’t be done for ethical reasons, but a correlation between smoking & cancer could be established from hospital records.
- Correlational analysis can give ideas for future research (eg. biological research on the effects of smoking).
- Correlation can even be used to test for reliability & validity (eg. by testing the results of the same test taken twice by the same ppl - a good reliable test will show a high correlation).
LIMITATIONS of Correlational research
- Correlational analysis cant establish ‘cause & effect’ relationships - it can only show that theres a statistical link between variables. Variables can be closely correlated w/o changes in one causing changes in the other - a third variable could be involved. Only a controlled experiment can show cause & effect.
- Care must be taken when interpreting correlation coefficients - high correlation coefficients could be down to chance. To decide whether a coefficient is significant, you have to use a proper significance test.
(for eg, the no. of births in a town was found to be positively correlated to the no. of storks nested in that town - BUT that doesnt mean that more storks caused the increase)
What are distributions
Distributions are graphs plotted to represent the average & spread of some characteristic of the population.
What does a normal distribution look like
- A normal distribution is symmetrical about the mean. (its shaped like a bell with its peak at the mean).
- This symmetry means the mean, median & mode are all the same.
- The width of the curve depends on the standard deviation & a different mean shifts the centre of the bell horizontally.
see pg118 for graph
A skewed distribution can either be
- Positive
- Negative
What is a skewed distribution
When there are scores that cluster tg at ether end of the data, it results in a skewed distribution.
What is a Positively skewed distribution
- If data is positively skewed, there is a cluster of scores at the lower end of the data set.
- The curve has a tail on the right side of the peak - it is said to be skewed to the right.
- The mode is less than the median, which is less than the mean.
- egs are reaction times, income, no. of children in family.
see pg119
What is a Negatively skewed distribution
- For a negative skew, there are more scores at the higher end of the data set.
- The tail is on the left side of the peak - it is skewed to the left.
- The mode is more than the median, which is more than the mean.
- Negative skew is less common but an eg is age at retirement.
see pg119
