Describing relationships using correlations
Download
1 / 22

Describing Relationships Using Correlations - PowerPoint PPT Presentation


  • 100 Views
  • Uploaded on

Describing Relationships Using Correlations. More Statistical Notation. Correlational analysis requires scores from two variables. X stands for the scores on one variable. Y stands for the scores on the other variable. Usually, each pair of XY scores is from the same participant.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Describing Relationships Using Correlations' - viola


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

More statistical notation
More Statistical Notation

Correlational analysis requires scores from two variables.

X stands for the scores on one variable.

Y stands for the scores on the other variable.

Usually, each pair of XY scores is from the same participant.


More statistical notation1
More Statistical Notation

  • As before, indicates the sum of the X scores, indicates the sum of the squared X scores, and indicates the square of the sum of the X scores

  • Similarly, indicates the sum of the Y scores, indicates the sum of the squared Y scores, and indicates the square of the sum of the Y scores


More statistical notation2
More Statistical Notation

Now, indicates the the sum of the X scores times the sum of the Y scores and indicates that you are to multiply each X score times its associated Y score and then sum the products.


Correlation coefficient
Correlation Coefficient

  • A correlation coefficient is the statistic that in a single number quantifies the pattern in a relationship

  • It does so by simultaneously examining all pairs of X and Y scores



Drawing conclusions
Drawing Conclusions

  • The term correlation is synonymous with relationship

  • However, the fact that there is a relationship between two variables does not mean that changes in one variable cause the changes in the other variable


Plotting correlational data
Plotting Correlational Data

  • A scatterplot is a graph that shows the location of each data point formed by a air of X-Y scores

  • When a relationship exists, a particular value of Y tends to be paired with one value of X and a different value of Y tends to be paired with a different value of X





Linear relationships
Linear Relationships Variables

  • A linear relationship forms a pattern that fits a straight line

  • In a positive linear relationship, as the scores on the X variable increase, the scores on the Y variable also tend to increase

  • In a negative linear relationship, as the scores on the X variable increase, the scores on the Y variable tend to decrease




Nonlinear relationships
Nonlinear Relationships Variables

In a nonlinear, or curvilinear, relationship, as the X scores change, the Y scores do not tend to only increase or only decrease: at some point, the Y scores change their direction of change.




Strength
Strength Variables

  • The strength of a relationship is the extent to which one value of Y is consistently paired with one and only one value of X

  • The larger the absolute value of the correlation coefficient, the stronger the relationship

  • The sign of the correlation coefficient indicates the direction of a linear relationship


Correlation coefficients
Correlation Coefficients Variables

  • Correlation coefficients may range between -1 and +1. The closer to 1 (-1 or +1) the coefficient is, the stronger the relationship; the closer to 0 the coefficient is, the weaker the relationship.

  • As the variability in the Y scores at each X becomes larger, the relationship becomes weaker


Computing the correlation coefficient
Computing the VariablesCorrelation Coefficient


Pearson correlation coefficient
Pearson Correlation Coefficient Variables

  • r used to describe a linear relationship between two scale variables


Spearman rank order correlation coefficient
Spearman Rank-Order VariablesCorrelation Coefficient

  • describes the linear relationship between two variables measured using ranked scores. The formula is

    where N is the number of pairs of ranks and D is the difference between the two ranks in each pair.


ad