correlations

• a correlation is a systematic association between the 2 continuous variables, age and beauty co-vary, as people get older they become more beautiful this is a positive correlation because the 2 variables increase together
• you may disagree and think that as people get older they become less attractive, you think age and beauty are systematically associated but it is a negative correlation, as one variable increases the other one decreases
• ceiling + floor effects: or you may simply feel that there is no relationship between age and beauty and this is called 0/no correlation
• correlational hypothesis: when conducting a study using a correlational analysis we need to produce a correlational hypothesis, this states the expected association between the co-variables (in an experiment we were considering the difference between 2 conditions of an independent variable)
• correlational hypothesis: in our example age and beauty are the co-variables so possible hypotheses might be 5 different points
• correlational hypothesis: 1. age and beauty are positively correlated (positive correlation, directional hypothesis)
• correlational hypothesis: 2. as people get older they are rated are more beautiful (positive correlation, directional hypothesis)
• correlational hypothesis: 3. as people get older their beauty decreases (negative correlation, directional hypothesis)
• correlational hypothesis: 4. age and beauty are correlated (positive or negative correlation, non-directional hypothesis)
• correlational hypothesis: 5. age and beauty are not correlated (0 correlation, non-directional hypothesis) this is actually a null hypothesis that states no relationship - not the same as no direction
• scattergrams: a correlation can be illustrated using a scattergram, for each person we obtain 2 scores which are used to plot 1 dot for that person - the co-variables determine the x and y position of the dot (x refers to the position on the x axis and y refers to the position on the y axis) the scatter on the dots indicates the degree of correlation between the co-variables
• correlation coefficient: if you plot a scattergram how do you know whether the pattern of dots represents a meaningful, systematic association? you can eyeball the graph and decide whether it looks like the dots form a line from top left to bottom right (strong negative correlation) or bottom left to top right (strong positive correlation)
• correlation coefficient: but this is a rather amateurish way of deciding whether there is a meaningful correlation, instead researchers use a statistical test to calculate the correlation coefficient a measure of the extent of correlation that exists between the co-variables
• correlation coefficient: a correlation coefficient is a number
• correlation coefficient: a correlation coefficient has a maximum value of 1 (+1 is a perfect correlation and -1 is a perfect negative correlation)
• correlation coefficient: some correlation coefficients are written w/ a minus sign (e.g. -52) whereas others are written w/ a plus sign (e.g. +52) the plus or minus sign shows whether it is a positive or negative correlation
• correlation coefficient: the coefficient (number) tells us how closely the co-variables are related
• correlation coefficient: there is 1 final step and that is to find out if our correlation coefficient is significant in order to do this we use tables of significance which tells us how big the coefficient needs to be in order for the correlation to count as significant (meaningful)
• evaluation S: correlations are used to investigate trends in data if a correlation is significant then further investigation is justified (such as experiments) if correlation is not significant then you can probably rule out a casual relationship
• evaluation S: as w/ experiments the procedures in a correlation can usually be easily repeated which means that the findings can be confirmed
• evaluation L: in a correlation the variables are simply measured, no deliberate change is made, therefore no conclusion can be made about 1 co-variable causing the other, consider e.g. a study that showed there was a positive correlation between students' attendance records at school and their academic achievements, a researcher couldn't conclude that the level of attendance caused the better achievement
• evaluation L: this is additionally a limitation because people assume casual conclusions, this is a problem because such misinterpretation of correlations may mean that people design programmes for improvement based on false premises e.g. a headteacher might mistakenly conclude that improving attendance would improve exam results
• evaluation L: furthermore the supposed casual connection may actually be due to intervening variables, unknown variables which can explain why the co-variables being studied are links, in our e.g. it might be that students who do not attend are the ones who dislike school and their dislike of school also impacts on exam performance, dislike of school may be the most important variable and there may well be others
• evaluation L: as w/ experiments a correlation may lack internal/external validity e.g. the method used to measure academic achievement may lack validity or the sample used may lack generalisability
• the strength of correlation research therefore lies in investigating the extent of relationships between variables which can be particularly useful in the early stages of research however it is imperative to avoid any casual inferences
• linear + curvilinear: the correlations we have considered are all linear - in a perfect positive correlation (+1) all the values would lie in a straight line from the bottom left to the top right
• linear + curvilinear: however there is a different kind of correlation - a curvilinear correlation, the relationship is not linear but curved there is still a predictable relationship
• linear + curvilinear: e.g. stress and performance do not have a linear relationship, performance on many tasks is depressed when stress is too high or too low, it is best when stress is moderate