Correlations Introduction

Learning Objectives Identify the features of correlations. Outline differences between positive and negative correlations and no correlations. Outline features of a correlation coefficient. The aim of this session will be to introduce correlations to students. Teacher to deliver information about positive and negative correlations (most students should be familiar from GCSE Maths, so teacher should encourage students to give information rather than passively receive it)

Key terms Correlation Positive correlation Negative correlation No correlation Correlation coefficient

Correlations Correlation: a measure of how strongly two or more variables are related to each other: Height is positively correlated to shoe size The taller someone is, the larger their shoe size tends to be. Like Self Report and Observation, there is no manipulation of data, conditions or groups in correlations. No IV or DV, just to co-occurring variables (co-variables). Teacher to stress the correct use of terminology: co-variables rather than IV and DV. Stretch & Challenge: If there is no IV, what can’t we establish?

Correlations Still use the same sampling methods: Volunteer, self selected, random, snowball Still consider the same ethical issues: How many of the ethical issues can you identify? Give an example of how each ethical issue may need to be considered in a correlation. Encourage students to recall how each of the sampling techniques would be used in addition to the ethical guidelines. Learners should be given a few minutes to recall independently, use a random name generator, or similar, to target students to share information

Unlike experiments there is no IV, just two variables that occur together as ‘co-variables.’ As there is no IV to manipulate we cannot establish cause and effect. We don’t know which variable is causing the other, we just know there is a relationship between them. DV IV Experiment CAUSE EFFECT

Unlike experiments there is no IV, just two variables that occur together as ‘co-variables.’ As there is no IV to manipulate we cannot establish cause and effect We don’t know which variable is causing the other, we just know there is a relationship between them. CoV CoV Correlation ? NO CAUSE & EFFECT

Correlations can be both the primary method or secondary technique. Self reports and observations can both be used as a way to gather data on variables, and then see if there is a relationship between them. Primary method: Correlations Secondary technique: Self report/Observation Experiments can compare the data between two groups using correlations. I find out men have a stronger correlation between age and time spent looking in the mirror than women. Primary method: Experiment Secondary technique: Correlation Students should be aware of the difference between correlation as a method and as a technique. Encourage students to think of examples of core studies that use correlation. Stretch and Challenge: which core study uses experiment as the method and correlation as the technique?

Task Activity 1: Identify other possible correlations we could investigate for age and sleep. Extension: Identify any two variables you would find interesting to investigate (you will be expected to conduct your own investigation at a later stage). Workbook activity 1 – Identifying correlations.

Positive and negative correlations Positive Correlation: as one variable increases, so does the other. Negative Correlation: as one variable increases, the other decreases. No Correlation: there is no relationship between the variables. Stretch and Challenge: The more revision is done, the higher the final grade is. Is this a positive or negative correlation?

Positive, negative and no correlations – Activity 2 Perfect Positive Relationship No relationship Perfect Negative Relationship Students could be asked how correlations are represented graphically and what positive, negative and no correlations look like on a graph. This can then be presented after activity 2.

Correlation Co-efficient We can measure the strength of the relationship, by using inferential statistics. Which statistical test would we need to use? Why? Being wealthy is correlated with living longer, BUT eating healthily and exercising has a stronger relationship with living longer. Correlation Coefficient: a number between -1 and 1 that tells us how strong the relationship is. Encourage students to explain the difference between inferential and descriptive statistics and the reasons for using each. They must also be able to demonstrate why a particular inferential test would be used (ordinal / interval level data, correlational design = Spearman’s Rho)

Correlation Co-efficient +1.0 perfect positive correlation +0.8 strong positive correlation +0.5 moderate positive correlation +0.3 weak positive correlation 0 no correlation -0.3 weak negative correlation -0.5 moderate negative correlation -0.8 strong negative correlation -1.0 perfect negative correlation

Task Complete Activity 3 in the workbook. Calculate the co-efficient for the data sets given. What can we conclude from the correlation co-efficient from this data?

Scatter diagrams and Evaluations Correlations Scatter diagrams and Evaluations

Learning Objectives Identify the features of scatter diagrams. Outline the different correlation hypotheses. Evaluate the strengths and weaknesses of correlations.

Scatter diagrams We can display correlation data in scatter diagrams. One variable (amount of revision done) along one axis and another variable (final grade) along the other. Each ‘point’ on the scatter diagram represents one participant: how much revision they put in and what their final grade was. Students will be given the opportunity to plot their own scattergraph, identifying the need to include titles and label axes

Amount of revision (in hours) Grade achieved A*-U Amount of revision (in hours) 2 5 7 10 Final grade U E C B A*

Amount of revision (in hours) Grade achieved A*-U We can then use the scatter diagram to describe the relationship between the variables Link back to correlation co-efficient. Get students to identify which correlation co-efficient would best fit here.

Task Complete Activity 4 in the workbook. Plot one variable on the x axis and one on the y axis. Plot using dots or crosses. Remember to include: Title Clearly labelled both axes (including measurements when possible). Students can use their data from activity 3, or they can use their own data.

Hypotheses Unlike Observation and Self Report we can generate hypotheses for Correlation Research. Recap: Null Hypothesis Alternate hypothesis (one tailed or two tailed). What is the difference between a one tailed and a two tailed hypothesis?

Hypotheses Correlations can’t show cause and effect Can’t mention the effect one variable will have on the other so we talk about the ‘relationship’ between two variables Still using the term significant Still must clearly state the variables and how they have been operationalised NEVER using the words cause, effect or difference.

Which word(s) must you NEVER use in a correlational hypothesis? Hypotheses Null hypothesis: there will be no relationship There will be no significant relationship between V1 and V2. Alternate hypothesis: One tailed: There will be a significant positive/negative relationship between V1 and V2 Two tailed: there will be a significant relationship between V1 and V2. Which word(s) must you NEVER use in a correlational hypothesis? ACTIVITY - Give examples of variables, cut up key words and variables and have students sort into the correct order (or line up each with a different word from the hypothesis)

Assessment Tasks Activity 5 - Complete the hypotheses questions in the workbook. Activity 6 - Answer the sample exam questions relating to correlations.

Evaluation Our correlation shows that ice-cream sales are positively correlated with murder rates. Do we think buying ice-cream causes people to commit murder? What third factor might make people more likely to buy ice creams and more likely to be angry and get in fights? Why would it be a problem not to consider alternative variables? Where in society do we tend to see correlation relationships described in causal terms?

Task Complete Activity 7. Mexican lemon imports prevent highway deaths Eating organic food causes autism From the buzzfeed article explain the correlations such as those above. There are many fun ways to demonstrate a correlation, one variable could be the students’ age in years and months or shoe size, while the other variable may be speed at completing a Sudoku puzzle (this may be good on a Monday morning to wake your students up). A fun and engaging way to introduce correlations is to look examples of how they can be misleading. There is an excellent post on buzzfeed which gives some great examples of real correlations http://www.buzzfeed.com/kjh2110/the-10-most-bizarre-correlations. This could be used as an IT task – students could explain the results, what interpretations there could be and why the results may be misleading.

Strengths of Correlations Makes a good pilot study to generate a hypothesis for an experiment. Can research variables that would be unethical to manipulate. Can understand the relationship between two variables (positive/negative, weak/strong).

Weaknesses of Correlations Correlations do not show causation. They have the same weakness as whatever method was used to gather the data (observation/self report). Tell us nothing about other variables that may be the real cause Often correlations are misleading: NEVER USE DIFFERENCE, EFFECT OR CAUSE when describing a correlation.

Correlations Practical Activity

Learning Objectives Carry out a practical activity on a correlation. Write a report for correlational research.

Report Writing You must complete a report for the correlation you have conducted Remember the procedure must be replicable. Students will recap the parts of a procedure using the accompanying matching activities if required.

Task You will now be carrying out your own correlational research. Follow the instructions from Activity 8 in the workook. You need to decide if you are using self report or observation to gather your data. Make sure your data can be plotted on a scale, not qualitative or nominal.

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