Workgroup notes with Experimental & Correlational Statistics at the Leiden University - 2018/2019


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      Experimental and Correlational Research: Summaries, Study Notes & Practice Exams - UL

      Lecture notes with Experimental and Correlational Research at the Leiden University - 2018/2019

      Lecture notes with Experimental and Correlational Research at the Leiden University - 2018/2019



      Lecture 1

      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  (rsdescribes 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
      Access: 
      JoHo members
      Workgroup notes with Experimental & Correlational Statistics at the Leiden University - 2018/2019

      Workgroup notes with Experimental & Correlational Statistics at the Leiden University - 2018/2019


      Week 1

       

      Prep exercises

      1. Which combination of measurement levels is required for the use of the Pearson, Spearman, and point-biserial correlation respectively?
      2. Which formula is suitable for calculating the Pearson, Spearman, and point-biserial correlations?
      3. Which formula describes the relationship between rpb and tindep?
      4. Which combination of measurement levels is required for the use of the phi coefficient?
      5. What is the specific formula for calculating the phi coefficient?
      6. Which formula describes the relationship between φ and χ2?
      7. What is the formula for testing the difference between two independent correlation coefficients?
      8. What is the rule of thumb for effect size r2 and r?

       

      Workgroup tips 1

      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

      Probability

      P

      p

      Standard Deviation

      σ

      S

      Correlation

      .....read more
      Access: 
      JoHo members
      What is a correlational research design?

      What is a correlational research design?

      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:

      • No manipulation: Researchers observe naturally occurring relationships between variables, unlike experiments where they actively change things.
      • Focus on measurement: Both variables are carefully measured using various methods, like surveys, observations, or tests.
      • Quantitative data: The analysis mostly relies on numerical data to assess the strength and direction of the relationship.
      • Types of correlations: The relationship can be positive (both variables increase or decrease together), negative (one increases while the other decreases), or nonexistent (no clear pattern).

      Examples of when a correlational research design is useful:

      • Exploring potential links between variables: Studying the relationship between exercise and heart disease, screen time and mental health, or income and educational attainment.
      • Developing hypotheses for further research: Observing correlations can trigger further investigations to determine causal relationships through experiments.
      • Understanding complex phenomena: When manipulating variables is impractical or unethical, correlations can provide insights into naturally occurring connections.

      Limitations of correlational research:

      • It cannot establish causation: Just because two things are correlated doesn't mean one causes the other. Alternative explanations or even coincidence can play a role.
      • Third-variable problem: Other unmeasured factors might influence both variables, leading to misleading correlations.

      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.

      What is the correlational method?

      What is the correlational method?

      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:

      • No manipulation of variables: Unlike experiments where researchers actively change things, the correlational method observes naturally occurring relationships between variables.
      • Focus on measurement: Both variables are carefully measured using various methods like surveys, observations, or tests.
      • Quantitative data: The analysis primarily relies on numerical data to assess the strength and direction of the relationship.
      • Types of correlations: The relationship can be positive (both variables increase or decrease together), negative (one increases while the other decreases), or nonexistent (no clear pattern).

      Here are some examples of when the correlational method is useful:

      • Exploring potential links between variables: Studying the relationship between exercise and heart disease, screen time and mental health, or income and educational attainment.
      • Developing hypotheses for further research: Observing correlations can trigger further investigations to determine causal relationships through experiments.
      • Understanding complex phenomena: When manipulating variables is impractical or unethical, correlations can provide insights into naturally occurring connections.

      Limitations of the correlational method:

      • Cannot establish causation: Just because two things are correlated doesn't mean one causes the other. Alternative explanations or even coincidence can play a role.
      • Third-variable problem: Other unmeasured factors might influence both variables, leading to misleading correlations.

      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.

      Summaries and study services for IBP Bachelor 1 at Leiden University - Year 2022/2023

      College- en werkgroepaantekeningen bij Experimenteel en Correlationeel Onderzoek - UL

      Collegeaantekeningen Experimenteel en Correlationeel Onderzoek, Psychologie Leiden
      Lecture notes with Experimental and Correlational Research at the Leiden University - 2018/2019

      Lecture notes with Experimental and Correlational Research at the Leiden University - 2018/2019



      Lecture 1

      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  (rsdescribes 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
      Access: 
      JoHo members
      Workgroup notes with Experimental & Correlational Statistics at the Leiden University - 2018/2019

      Workgroup notes with Experimental & Correlational Statistics at the Leiden University - 2018/2019


      Week 1

       

      Prep exercises

      1. Which combination of measurement levels is required for the use of the Pearson, Spearman, and point-biserial correlation respectively?
      2. Which formula is suitable for calculating the Pearson, Spearman, and point-biserial correlations?
      3. Which formula describes the relationship between rpb and tindep?
      4. Which combination of measurement levels is required for the use of the phi coefficient?
      5. What is the specific formula for calculating the phi coefficient?
      6. Which formula describes the relationship between φ and χ2?
      7. What is the formula for testing the difference between two independent correlation coefficients?
      8. What is the rule of thumb for effect size r2 and r?

       

      Workgroup tips 1

      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

      Probability

      P

      p

      Standard Deviation

      σ

      S

      Correlation

      .....read more
      Access: 
      JoHo members
      Experimenteel en Correlationeel Onderzoek: Samenvattingen, uittreksels, aantekeningen en oefenvragen - UL
      Click & Go to related summaries or chapters

      Study guide with lecture notes for Psychology Bachelor 1 at Leiden University

      Lecture notes with Psychology Bachelor 1 at Leiden University

      Table of content

      • Workgroup notes with Personality, Clinical and Health Psychology - 2018/2019
      • Workgroup notes with Inferential Statistics - 2018/2019
      • Lecture notes with Experimental and Correlational Research - 2018/2019
      • Workgroup notes with Experimental and Correlational Research - 2018/2019
      • Lecture notes with Social and Organizational Psychology - 2018/2019
      • Lecture notes with Developmental and Educational Psychology - 2018/2019
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      Study guide with lecture notes for Experimental and Correlational Research at the Leiden University

      Study guide with lecture notes

      Lecture notes with Experimental and Correlational Research

      • For lecture notes and workgroup notes
      • see the supporting content of this study guide
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      Lecture notes Experimental and Correlational Research

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