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Workgroup notes with Experimental & Correlational Statistics at the Leiden University - 2018/2019
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6/2/2019
-Correlation is about two variables being associated, but there is no evidence of causality.
-Causality however requires multiple factors: covariance (variables have an association), directionality(cause precedes effect (in time)) and internal validity(eliminate alternative explanations).
- Correlations can be displayed in scatterplots that show:
- Direction: positive or negative
- Strength: density of the points
- Shape: linear/nonlinear and homogeneous (one cluster) / heterogeneous (multiple clusters).
- Outliers
-Covariance (sxy): to measure the degree to which two variables vary together.
Formula: sxy = Σ(xi-x)(yi-y) / N-1
It provides us with information on the strength and direction of the association. The disadvantage is that the covariance is dependent on the unit of measurement of the variables.
-Pearson r is a standardized measure that describes the linear relationship between two quantitative variables, and always lies between -1 and +1.
Formulas: r = sxy / sxsy Alternative: r = Σzxzy / N-1
- Remember that a z-score is a standardized score that displays how many standard deviations a certain score is away from the mean.
Alternative correlational techniques:
- The Pearson r is the correlation coefficient that is most commonly used. There are alternatives:
quantitative + quantitative --> Pearson r
ordinal + ordinal --> Spearman’s rho (rs)
dichotomous(only two possible values)+ quantitative --> point-biserial correlation (rpb)
dichotomous + dichotomous --> phi coefficient (ϕ)
-Spearman’s rho (rs) describes relationship between two ordinal variables/ranked scores.
Formulas: xrank = N + 1 / 2 srank = √ (N(N+1) / 2)
rs = r on ranked data
Spearman’s rho is also an alternative to Pearson r in case of outliers and/or weak non-linearity.
-Point-biserial correlation describes relationship between quantitative and dichotomous variables. We use the Pearson correlation formula to calculate rpb: rpb = r
The sign of the correlation (+/-) depends on the way 0 and 1 are assigned to groups.
Relationship rpb and tindependent: rpb = Square root of t2 / t2 + df
-Phi-coefficient (ϕ) describes relationship between two dichotomous variables: ϕ
.....read more
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 |
A correlational research design investigates the relationship between two or more variables without directly manipulating them. In other words, it helps us understand how two things might be connected, but it doesn't necessarily prove that one causes the other.
Imagine it like this: you observe that people who sleep more hours tend to score higher on tests. This correlation suggests a link between sleep duration and test scores, but it doesn't prove that getting more sleep causes higher scores. There could be other factors at play, like individual study habits or overall health.
Here are some key characteristics of a correlational research design:
Examples of when a correlational research design is useful:
Limitations of correlational research:
While correlational research doesn't provide definitive answers, it's a valuable tool for exploring relationships and informing further research. Always remember to interpret correlations cautiously and consider alternative explanations.
In the realm of research methodology, the correlational method is a powerful tool for investigating relationships between two or more variables. However, it's crucial to remember it doesn't establish cause-and-effect connections.
Think of it like searching for patterns and connections between things, but not necessarily proving one makes the other happen. It's like observing that people who sleep more tend to score higher on tests, but you can't definitively say that getting more sleep causes higher scores because other factors might also play a role.
Here are some key features of the correlational method:
Here are some examples of when the correlational method is useful:
Limitations of the correlational method:
While the correlational method doesn't provide definitive answers, it's a valuable tool for exploring relationships and informing further research. Always remember to interpret correlations cautiously and consider alternative explanations.
In de bijlagen vind je collegeaantekeningen van hoorcolleges en werkgroepen 1 t/m 7 van Experimenteel en Correlationeel Onderzoek, onderdeel van de bachelor Psychologie aan de Universiteit Leiden:
6/2/2019
-Correlation is about two variables being associated, but there is no evidence of causality.
-Causality however requires multiple factors: covariance (variables have an association), directionality(cause precedes effect (in time)) and internal validity(eliminate alternative explanations).
- Correlations can be displayed in scatterplots that show:
- Direction: positive or negative
- Strength: density of the points
- Shape: linear/nonlinear and homogeneous (one cluster) / heterogeneous (multiple clusters).
- Outliers
-Covariance (sxy): to measure the degree to which two variables vary together.
Formula: sxy = Σ(xi-x)(yi-y) / N-1
It provides us with information on the strength and direction of the association. The disadvantage is that the covariance is dependent on the unit of measurement of the variables.
-Pearson r is a standardized measure that describes the linear relationship between two quantitative variables, and always lies between -1 and +1.
Formulas: r = sxy / sxsy Alternative: r = Σzxzy / N-1
- Remember that a z-score is a standardized score that displays how many standard deviations a certain score is away from the mean.
Alternative correlational techniques:
- The Pearson r is the correlation coefficient that is most commonly used. There are alternatives:
quantitative + quantitative --> Pearson r
ordinal + ordinal --> Spearman’s rho (rs)
dichotomous(only two possible values)+ quantitative --> point-biserial correlation (rpb)
dichotomous + dichotomous --> phi coefficient (ϕ)
-Spearman’s rho (rs) describes relationship between two ordinal variables/ranked scores.
Formulas: xrank = N + 1 / 2 srank = √ (N(N+1) / 2)
rs = r on ranked data
Spearman’s rho is also an alternative to Pearson r in case of outliers and/or weak non-linearity.
-Point-biserial correlation describes relationship between quantitative and dichotomous variables. We use the Pearson correlation formula to calculate rpb: rpb = r
The sign of the correlation (+/-) depends on the way 0 and 1 are assigned to groups.
Relationship rpb and tindependent: rpb = Square root of t2 / t2 + df
-Phi-coefficient (ϕ) describes relationship between two dichotomous variables: ϕ
.....read more
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 |
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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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