IPR 2

What are the two ways correlation can be written?

r or p

What is the definition of correlation?

An inferential statistical test used to determine whether there is a significant relationship between two variables

What is the purpose of correlation?

Assess the strength and direction of association by comparing how scores in two different variables change

What is the test output of correlation?

• Correlation coefficient which represents strength and direction of relationship

• P-value to test if observed relation is statistically significant

Does correlation have independent and dependent variables?

No both variables treated equally

What are the controls for correlation?

• No experimental manipulation

• No control of variables

• No random assignment of participants to groups

What is a positive correlation also known as?

Direct relationship

What is a negative correlation also known as?

Inverse relationship

How can a positive correlation be explained?

• Two variables move in the same direction

• When variable A increases, variable B does too

How can a negative correlation be explained?

• Two variables move in opposite direction

• When variable A increase, variable B decreases

Why visualise data with a scatterplot?

• Shows positive or negative slope

• General impression of correlation

• Outliers

What is the line of ‘best fit’?

General pattern of the data

What are the differences in the slope if there is a positive or negative correlation?

Positive - line slopes upwards

Negative - line slopes downwards

When can no correlation be determined?

Points are scattered without a pattern

What is the range of the correlation coefficient?

-1 to +1

What is a +1/-1 relationship?

+1 = perfectly positive

-1 = perfectly negative

What are the r coefficients for relatively small, typical and relatively large? (Cohen standard)

• 0.1

• 0.3

• 0.5

What is the difference between one-tailed and two-tailed hypothesis?

One tailed - expect to find a positive or negative relationship

Two tailed - expect a relationship but do not specify positive or negative

What is important to remember about correlation?

Just because there is a significant relationship does not mean one CAUSES the other

Benefits of correlation?

• Identify and explore relationships

• Test hypothesis

• Make predictions

• When you can’t do experiments ethically

• Starting point for experiments

• Simplifies complex relationships

What kind of test do we do if assumptions are met?

Parametric

What kind of test do we do if assumptions are not met?

Non-parametric

What type of tests are chi-square?

Non-parametric as works with minimal assumptions (categorical data not normally distributed)

Why do assumptions matter?

Ensure test is appropriate and conclusions are reliable

Parametric tests are usually?

• more efficient and powerful

• more precise and accurate

• higher chance of detecting a true effect

What are the two types of correlation test?

• Pearson’s r correlation

• Spearman’s rank (Spearman’s rho)

What is the parametric correlation test?

Pearson’s r correlation

What is the non-parametric correlation test?

Spearman’s rank

What are the four assumptions of correlation?

Linearity - linear relationship between variables

Normality - data are approx. normally distributed (symmetric)

Type of data - continuous (interval or ratio sometimes ordinal)

Outliers - no extreme outliers

What type of data can a correlation not be run on?

Categorical and nominal

What two assumptions are most important?

Linearity and outliers

What is a monotonic trend?

Consistent movement (steepness can change)

What does the correlation coefficient tell you?

Number - strength or size of relationship

Sign - direction of relationship

Default alpha level of significance?

0.05

What to do is p<a?

Significant relationship, reject null

What to do is p>a?

Not significant, fail to reject null

Why is an experimental design used?

To determine the relationship between an independent variable and dependent variable

What does experimental design all us to draw conclusions about?

Cause-and-effect relationships

What is a t-test?

Statistical test used to determine whether there is a significant difference between the means of two groups

What is the purpose of a t-test?

Assess whether the average score of a dependent outcome differs between two groups

What does the test statistic show (t)?

The size of the difference between group means relative to varaibility

What is high variability?

The data from one or both groups is noisy, moving around a lot and difference may just be randomness

Why do we want a low variability?

Want any difference between groups to be (mostly) explained by our experimental observations

What does it mean that significant difference between two groups?

Larger ‘between’ group differences and smaller ‘within’ group variance

What are the assumptions of t-tests?

Independent observations - Each participants score does not influence on the score of another participant

Normality - Data is approx. normally distributed

Homogeneity of variance - variance (spread of data) should be equal in the two groups

Type of data and outliers - not strict

How can we experimental manipulate data?

• Increasing between-group variance

• Decreasing within-group variance

What does a t-test tell you?

If there is a big enough difference compared to the natural variability between the groups - basically is the experimental manipulation (IV) causing significant changes to the DV

What is the equation for t?

t = difference between the groups / variability within groups

How will a greater difference between groups compared to variability be seen in the t-statistic?

It will be larger - statistically significant result

What are the three types of hypothesis in t-tests?

Alternative (one tailed) (directional) - where difference lies

Alternative (two tailed) (non-directional) - a difference exists

Null Hypothesis - no difference between groups

What are the benefits of t-tests?

• Identify differences between groups

• Test hypotheses about whether groups truly differ

• Experimental - controlled conditions

• Make predictions

• Starting point for other experiments

What are the three types of t-tests? parametric

Paired, independent and one-sample

How many groups or conditions in the IV?

Two - paired or independent

One - one sample

Who are the participants? (Two)

Same in each condition - paired

Different in each condition - independent

How to calculate variability (one sample)?

Difference - between mean of single group and known pop

Variability - within sample

How to calculate variability (paired)?

Mean difference between two measures from same group

Variability - difference between scores how each person changed

How to calculate variability (independent)?

Difference - Means of two independent groups

Variability - Pooled within-group variability

How to test for normality?

Shapiro-Wilk

How to test for homogeneity of variance?

Levene’s test or violated use Welchs

What is the homogeneity of variance assumption?

Variance approx equal

How is a non-parametric different from parametric (data)?

Rank the raw data

What two non-parametric t tests use Wilcoxon signed rank test?

One sample and paired

What non-parametric t test uses Mann-Whitney U test?

Independent

Explain how variability is different in one sample t test and paired?

• median of difference

• Ranked differences for variability

Explain how variability is different in independent?

Difference - if one group has higher rank than other

Variability - combined rank ordering variability

Difference in presenting data for parametric vs non?

P - report mean and s.d., use bar chart or boxplot

NP - report median and IQR, box and whisker or violin