Statistics 1 1 Correlations Definitions: A correlation is measure of association between two quantitative variables with respect to a single individual A correlation coefficient is a descriptive statistic that quantifies the degree of the association between two variables
23
Embed
Statistics 11 Correlations Definitions: A correlation is measure of association between two quantitative variables with respect to a single individual.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Statistics 1 1
Correlations
Definitions:
A correlation is measure of association between two quantitative variables with respect to a single individual
A correlation coefficient is a descriptive statistic that quantifies the degree of the association between two variables
The same set of n = 6 pairs of scores (X and Y values) is shown in a table and in a scatterplot. Notice that the scatterplot allows you to see the relationship between X and Y.
Examples of positive and negative relationships. (a) Beer sales are positively related to temperature. (b) Coffee sales are negatively related to temperature.
(a) shows a strong positive relationship, approximately +0.90; (b) shows a relatively weak negative correlation, approximately –0.40; (c) shows a perfect negative correlation, –1.00; (d) shows no linear trend, 0.00.
The coefficient of determination is a measure of the proportion of variance that can be accounted for in one variable because of its association with another variable
Calculation:
Square the Pearson Product-moment Correlation Coefficient
• Given a correlation of r = +0.5 between IQ and reading speed
• The coefficient of determination (r²) says that 25% of the variation in the reading speed of your subjects is related to the variability in their individual IQ's
• Which also means that 75% of the variation in reading speed of your subjects is related to some other factor(s), i.e. 1 - r²
The logic of the test is then simple If the differences between O and E are small, chi-
square will be smallIf the differences between O and E are large, chi-
square will be largeAnd if chi-square is large enough
– Your conclusion will be that the observed frequencies are such that your sample does not come from the population from which the null hypothesis was derived
Question: Does "post position" (1-8) make and difference in the outcome of horse racing?Data: Observe 144 races and record starting post position of winner