Validity: Suppose we have developed a new test of intelligence.Thus, we predict high SAT scores will lead to high GPA scores, and conversely. We can use the value of one variable that is known now to predict the value that the other variable will take on in the future.įor example, we require high school students to take the SAT exam because we know that in the past SAT scores correlated well with the GPA scores that the students get when they are in college. If two variables have been known in the past to correlate, then we can assume they will continue to correlate in the future. Prediction: Correlations can be used to help make predictions.The relationship between drive ratio and MPG is weekly positive, though not zero. The Pearson correlation coefficient is -.59. The relationship between drive ratio and Horsepower is weekly negative, though not zero. The Pearson correlation coefficient is +.92. The relationship between Weight and Horsepower is strong, linear, and positive, though not perfect. that +1.00 is the largest postive correlation and -1.00 is the largest negative correlation that is possible. There are strengths in between -1.00, 0.00 and +1.00. No relationship: When two variables have no relationship at all, their correlation is 0.00.They are said to be perfectly linearly related, either positively or negatively. Perfect Relationship: When two variables are exactly (linearly) related the correlation coefficient is either +1.00 or -1.00.The mesures we discuss only measure the strength of the linear relationship between two variables. The Degree (Strength) of a Relationshipįinally, a correlation coefficient measures the degree (strength) of the relationship between two variables.There are other correlation coefficients that measure curvilinear relationship, but they are beyond the introductory level. In this course we only deal with correlation coefficients that measure linear relationship. An example of the relationship between the Miles-per-gallon and engine displacement of various automobiles sold in the USA in 1982 is shown below. Curvilinear: A curved relationship is called curvilinear, because it approximates a curved line.The GPA, MathSAT example shows a relationship that is, roughly, a linear relationship. Linear: A straight relationship is called linear, because it approximates a straight line.The form or shape of a relationship refers to whether the relationship is straight or curved. Postive relationships have a "plus" sign, whereas negative relationships have a "minus" sign. The direction of the relationship between two variables is identified by the sign of the correlation coefficient for the variables. Negative: In a negative relationship the variables tend to move in the opposite directions: If one variable increases, the other tends to decrease, and vice-versa.As GPA (or MathSAT) increases, the other variable also tends to increase. In the example above, GPA and MathSAT are positively related. If one decreases, the other tends to also. Positive: In a positive relationship both variables tend to move in the same direction: If one variable increases, the other tends to also increase.The direction can be positive or negative. The correlation measure tells us about the direction of the relationship between the two variables. They can tell us about the direction of the relationship, the form (shape) of the relationship, and the degree (strength) of the relationship between two variables. 32.Ĭorrelations have three important characterstics. Note that the Pearson correlation (explained below) between these two variables is. Note that is to the right of MathSAT of 710 and above GPA of 2.30. This student is represented in the scatterplot by high-lighted and labled ("5") dot in the upper-left part of the scatterplot. Each individual is identified by a single point (dot) on the graph which is located so that the coordinates of the point (the X and Y values) match the individual's X (GPA) and Y (MathSAT) scores.įor example, the student named "Obs5" (in the sixth row of the datasheet) has GPA=2.30 and MathSAT=710.
The scatterplot has the X values (GPA) on the horizontal (X) axis, and the Y values (MathSAT) on the vertical (Y) axis. Here are the Math SAT scores and the GPA scores of 13 of the students in this class, and the scatterplot for all 41 students: The pairs of scores can be listed in a table or presented in a scatterplot.Įxample: We might be interested in the correlation between your SAT-M scores and your GPA at UNC. These scores are normally identified as X and Y. The correlation requires two scores from the same individuals. Usually the two variables are simply observed, not manipulated. Correlation is a statistical technique that is used to measure and describe a relationship between two variables.
0 kommentar(er)
