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Prep exercises
Correlation is NOT causation. It is an association between variables.
Positive correlation = both increase or decrease
Negative = One increases, the other decreases
Pearson’s r; both variables are at an interval level. Formula: ∑ZxZy/n-1
Spearman rho = two ordinal variables (To avoid outlier influence in Pearson’s r) rs = r Important: RANK IT FIRST, then take the z scores
Point Biserial; one dichotomous and one continuous variable rpb = r
Phi is a nominal variable, that only has two levels each aka dichotomous X2 = r
Dichotomous means that the value can only be one of two things. For instance yes/no, male/female, left/right. It is a nominal variable, but where with a simply nominal variable answers can be red/blue/green/yellow, a dichotomous variable could in this case only be red/blue, for instance.
Basically, all of these correlation have the basic formula, which is ∑ZxZy/n-1
R is about sample, ρ is population
Parameter | Population | Sample |
Mean | µ | x̄ |
Probability | P | p |
Standard Deviation | σ | S |
Correlation | Ρ | r |
In order to see if the r you have calculated is useful for the population, use the formula
t = (r √N-2) / √(1 - r2)
Correlation type | Type of variables | Correlation symbol | Formula |
Pearson’s r | Interval/Interval | r | ∑ZxZy/n-1 |
Spearman’s rho | Ordinal/Ordinal | rs | ∑ZxZy/n-1 |
Point Biserial | Dichotomous/Interval | Rbp | ∑ZxZy/n-1 |
Phi | Dichotomous/ Dichotomous | Φ | ∑ZxZy/n-1 |
Difference between correlation and regression: regression predicts a value, correlation is not causation.
B0 , also called the intercept, and it is the mean of y when x is 0
B1, also called regression coefficient, is the slope.
Simple regression has only one predictor, multiple regression has multiple predictors.
When the slope increases, the regression line gets steeper.
When the intercept increases, the entire line gets lifted a bit.
Why do we test the regression coefficient?
If a question says ‘weight’ as a function of ‘height’, in which case height is X and weight is Y.
The error of observed – predicted is called residual.
For the bigger picture, look at it like this example:
A teacher wants to know how the grades of his students are composed. He supposes that intelligence is a big part of the grade of student and so draws up a correlation between the grade and the student’s intelligence (week 1, correlations). But, after calculating the correlation, he supposes that genetics and effort also have an impact on the grade. These parts, genes, intelligence and effort, are called predictors (week 2) and each influence the dependant variable – the grade. But, the teacher later supposes that while genetics and intelligence both have an influence on the grade, genetics also have an influence on intelligence (week 3). To take out these influences, you calculate unique contributions.
Prep exercises
When working in SPSS and asked to calculate any of the correlations from Week 1, simply go to Analyse -> Bivariate -> Calculate all variables with Pearson’s r
When SPSS’ scatterplot gives a proper curved line, you can assume Pearson’s r is not a correct correlation to use, because the correlation is not linear. This means that you have to use a nonparametric correlation such as Spearman’s rho.
Coefficientsa | |||||||||||||||
Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | 95.0% Confidence Interval for B | Correlations | |||||||||
B | Std. Error | Beta | Lower Bound | Upper Bound | Zero-order | Partial | Part | ||||||||
1 | (Constant) |
1.163 = B0
| .007 |
| 177.296 | .000 | 1.150 | 1.176 |
|
|
| ||||
lskin | -.063 = B1 |
.004
| -.849 | -15.228 | .000 | -.071 | -.055 | -.849 | -.849 | -.849 | |||||
a. Dependent Variable: den |
When you want a regression line in a scatter plot, open the chart builder, go to elements and click ‘fit line to total’. In the window that opens, select ‘linear’ and choose whether you want an regression line of the mean or from individual.
When you want to run a regression analysis in SPSS, go to Analyse -> Regression -> Linear. There, your x axis is your independent and your y is the dependent.
A dummy variable in SPSS tells you the difference in intercepts (b0).
Something called and ‘interaction’ is always a multiplication.
When you want to centre a variable, you do the following steps:
Y^= B0(intercept) + B1 (slope) – b2 (difference in intercept) – b3 (difference in slope
ANOVA is technically a t-test on steroids, you use it to measure the type 1 error difference between different groups/variables. With ANOVA, you can claim causation, rather than correlation.
Effect parameter means that you see how far your mean is removed from the grand mean. You get the grand mean by taking the average of all means.
The closer points in a scatterplot are to the mean, the less error you have. Error = Xij – XmeanJ
A higher ANOVA result aka a higher F means a lower p and thus more significance. More significance means that there is a difference between at least two means.
Overview of this workgroup: how to test which means are influencing the difference.
Priori test is beforehand -> clear what you are testing, BUT, you have to use a Bonferroni Correction to correct your Type 1 error (the chance that you reject H0 even though it is correct)
A Post Hoc test you perform after, and SPSS makes the correction for type 1 error for you.
Setting your contrast positive means that you give the positive score to the side that you expect the highest mean of.
All the added weights (proportions), need to add up to 0. This means that you devide your probabilities so that your mean percentages add up to +1 on the one side and -1 on the other.
Independence of Contrasts is the table to see if the contrasts are actually independent, to narrow down the clusters so you test everything a bit.
When comparing contrast, multiply the contrasts of conditions and add them up to each other. This has to also equal 0
When working with the effect parameters α, β, and αβ, first make a contingency table that looks like this (in case of a 2x3 factorial design)
- | Condition A1 | Condition A2 | Condition A3 |
|
Condition B1 | Mean Score B1xA1 | Mean Score B1xA2 | Mean Score B1xA3 | Mean of B1 |
Condition B2 | Mean Score B2xA1 | Mean Score B2xA2 | Mean Score B2xA3 | Mean of B2 |
| Mean of A1 | Mean of A2 | Mean of A3 | Mean of all means |
Hypothesis of the table would be
H0 : αβji = 0
Keep in mind that with contrasts in SPSS, you should not include the missing variable. When asked for unique or alone variance, use part/partial correlation and square it
Week 1
Week 2
b1 = sxy/sx2 =r * (sy/sx)
Week 3
Week 4
SEx bar = se 1+ (1/N) + ((x – xbar)2/(N-1)s2x
Week 5
Week 6
Source Sum of Squares DF Mean Square F
Groups Pni (y¯i − y¯) 2 = Pniαˆ 2 i ) I − 1 SSG/DFG MSG/
Week 7
Week 8
GOOD LUCK ON THE EXAM!!
Xx Emy
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Exam Tips JulitaBonita contributed on 07-03-2019 11:06
A now 2nd year IBP student, shared her exam tips for this course last year. Check out the relevant content > IBP Leiden-Experimental and Correlational Research. You can also follow Ilona's profile for more summaries, blogs and lecture notes.
Lecture notes Experimental and Correlational Research Psychology Supporter contributed on 28-03-2019 16:37
Also interested in reading the complementary lecture notes for the course this year? Check out Noa's profile for relevant content!
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