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School

Macquarie University
Department

Psychology

Course Code

PSY248

Professor

Eugene Chekaluk

Study Guide

Final

CORRELATION/REGRESSION

Before statistics;

â€¢ Step 1: understand the research question

â€¢ Step 2: how are DV and IV measured?

â€¢ Step 3: choose method of analysis (correlation/regression)

Conduct correlation/regression analysis;

â€¢ Part 1: univariate

â€¢ Part 2: bivariate

â€¢ Part 3: regression and check assumptions

â†’ Correlation asks is there a RELATIONSHIP between two variables

â†’ Regression refers to PREDICTION

UNIVARIATE

Step 1: understand research question

Example:

â€¢ IV = age of carer

â€¢ DV = carer distress

â€¢ 1. What is the level of carer distress? Does carer distress vary? (univariate)

o Produce descriptive statistics

â€¢ 2. Is carer distress (linearly) related to age of carer? (bivariate)

o Produce correlational statistics

â€¢ 3. Does knowledge about age help predict level of carer distress? (regression)

o Produce regression

â€¢ This is NON-EXPERIMENTAL research

Step 2: how are the DV/IV measured?

â€¢ We look at

o How we intended to measure (questionnaire)

o What we actually ended up with (results â€“ data)

â€¢ Decide level of measurement â€“ categorical, ordinal or interval

â€¢ Then we need this to decide what statistical analysis to use

â€¢ This leads to either correlation/regression = IV/DV continuous/interval/numeric and normal

â€¢ For instance:

o Age: categorical (young, middle, old), distress: categorical (low, medium, high) = chi-

square appropriate

o Age: categorical (young, middle, old), distress: numerical = one-way ANOVA

o Age: numerical, distress: numerical = correlation/regression

â€¢ Specific Health Questionnaire; consisted of 15 items

o Study had age categories (one of 9) â€“ but we are going to treat them as continuous

variables (numeric)

Step 3: choose method of analysis

â€¢ Produce histograms and describe them based on 5 assumptions

Assumptions of normality:

â€¢ Central tendency

o Typical or average score, centre of distribution, peak in the distribution â€“ does it exist?

â€¢ Variability (SD and range)

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o Do all the cases tend to score at about the same point or are they widely scattered â€“

width of distribution

â€¢ Skewness

o Symmetry vs. lopsidedness of distribution

o Positive (right) skew, negative (left) skew, symmetric distributions have no skew

o Symmetry/Standard error of skew = symmetrical (between -2 and +2 = unskewed)

â€¢ Kurtosis

o Flatness or peakness of a distribution. Platykurtic (flat), leptokurtic (very peaked) and

mesokurtic (a normal distribution)

o Kurtosis = kurtosis/standard error of kurtosis

â–ª Between -2 and +2 = mesokurtic

â€¢ Modal characteristics (modality)

o Frequency of peaks as unimodal, bimodal or multimodal

o A distribution with no mode is a uniform or rectangular distribution

o In general, the presence of more than one frequency peak (mode) in a distribution

means that the data represent several relatively homogenous subgroups within the

larger sample being studied

o You want your distribution to be unimodal â€“ indicates homogeneity

USING SPSS

â€¢ Use the frequencies command to produce graphical and numeric summaries of all five

possible DVs

â€¢ Analyse â†’ descriptive stats â†’ frequencies

o Ask for all the 5 diff histogram characteristics

â€¢ Pasted syntax created by filling out point and click dialogue boxes

â€¢ Ask questions based on graphical summary

o Central tendency â€“ yes

o Variability â€“ yes

o Kurtosis â€“ mesokurtic

o Skewness â€“ no skew

o Modality â€“ unimodal

BIVARIATE

â€¢ Create scatterplot and Pearsonâ€™s r in SPSS

Use SPSS point and click to produce scatterplot

â€¢ Graphs (legacy dialogs) â†’ scatter â†’ simple â†’ define

â€¢ Simple scatterplot â†’ put DV on Y axis, IV on X axis

Scatterplot (7 Assumptions)

1. Linear Relationship (straight line)

â€¢ Increase or decrease in the same direction, and at the same rate

2. Monotonic Relationship

â€¢ Increase or decrease in the same relative direction, but not at the same rate

3. Outliers

4. Gaps

5. Direction of the function that describes relationship between 2 variables

â€¢ Positive, negative, or no relationship

6. Effect of X on Y (slope): the steeper the slope, the greater the effect

â€¢ Do the points cluster around the imaginary straight line?

7. Correlation (strength of relationship)

â€¢ Â±0.3 â€“ weak

â€¢ Â±0.5 â€“ moderate

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â€¢ Â±0.7 â€“ strong

â†’ Provided we are happy that all 7 steps are okay, we can appropriately summarise the relationship

numerically by calculating a (Pearson) correlation

Analyse â†’ Correlate â†’ Bivariate

â€¢ Pearson correlation

â€¢ Numeric summary table appears of Pearsonâ€™s correlation coefficient between the two

variables

â€¢ -.5 = confirms negative relationship from scatterplot (found in Pearson correlation/SHTOT);

if they were both -1; all dots would be plotted on the line perfectly

o Also explains weak/moderate correlation

â€¢ As a rule of thumb, say:

o Correlations between 0 and 0.29 (pos and neg) are â€˜weakâ€™

o Correlations between 0.30 and 0.59 are â€˜moderateâ€™

o Correlations between 0.60 and 1.00 are â€˜strongâ€™

â€¢ Significance depends on two things

o The size of the relationship AND

o The sample size

Five points about correlations:

1. Note that SPSS reports that our correlation is significant ( p <0.0005)

â€¢ Significance = population correlation is not equal to zero

â€¢ If sig. 2 tailed states .000 = you cannot conclude that it is 0% as it may go beyond the

decimals

2. If asked, SPSS will always calculate a linear correlation even when appropriate to do so.

Always inspect bivariate scatterplot first to determine that a linear correlation is appropriate.

3. R = 0.00 does not always mean NO correlation, it means no LINEAR correlation

4. Always report ranges of X and Y â€“ we do not know what happens to relationship beyond

range of our data

5. Correlation does not imply causation

REGRESSION

â€¢ Regression = prediction

â€¢ F or t statistic represents the prediction (F = ï¿½î¬¶)

o If it is significant:

â–ª Write and interpret regression equation (of line going through scatterplot)

â–ª Comment on and interpret îœ´î¬¶%

â–ª Check 4 assumptions of regression

Syntax SPSS:

REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA

/CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT shtot /METHOD=ENTER age

1. Equation of the straight line

â€¢ Unstandardised B coefficients â†’ conform to general equation of a line

â€¢ Regression equation

o Predicted distress = y-axis intercept + slope (age/independent variable)

â–ª Y-axis intercept = the constant (identified from coefficient table); this number

will be the point where the line would cross the y-axis

â–ª Always make sure you write PREDICTED (as there can still be error)

â–ª Use info under B to write down those values into the equation

â–ª E.g. predicted distress = 38.25+(-2.62)(age)

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