hypothesis of association: correlation chapter 11
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Hypothesis of Association: CorrelationChapter 11
Difference vs. Association
Hypothesis of Association
• relationship between two sets of variables are examined to determine whether they are associated or correlated
-IV is not manipulated but assigned
-can not determine cause and effect
-Correlation
Hypothesis of Difference
• A deliberate manipulation of a variable to see if a difference in behavior occurs
-IV is not assigned but manipulated
-can determine cause-and-effect relationships
-Experiment
Correlation: a measure of the relationship between two variables-correlation coefficient (r): a number calculated from the formula for measuring a correlation
*indicating strength & direction *ranges from +1 to -1 -strong relationship if the correlation coefficient is close to +1 or -1
*knowing the relationship between two variables allows us to make predictions -EX: if you study X amount of hours, a score of X is predicted
-positive correlation *represented by a positive # (0 to +1) *as the value of one variable increases, the other variable also increases
-EX: study time goes up, test scores go up OR as study time goes down, test scores go down-negative correlation
*represented by a negative # (0 to -1) *as the value of one variable increases, the other variable decreases
-EX: as study time goes up, party time goes down-zero correlation
*represented by 0 *no relationship between variables
-EX: study time & height
Correlation
Study Time
Exam
Sco
res
Exam
Sco
res
Party Time
r =-0.6321
Correlation: Scatter Plots
Exam
Sco
res
Height
r =0.8273
• Formula:
• Calculation
Step 1: Calculate the means
Step 2: Calculate the standard deviations
Step 3: Plug all values into the formula
Correlation: Pearson r
• Testing a hypothesis using correlation
-r refers to the sample correlation and ρ (rho) refers to the population correlation
Ho: ρ = 0 there is no correlation in the population
Ha: ρ ≠ 0 there is a correlation in the population
• Critical Values (Table E)
-df are N-2 (number of pairs of score minus 2)
-if the calculated r value is greater than or equal to the table r value then reject Ho
-NOTE: as sample size increases, really small correlations become significant
**EX: look at df=400
• Guilford’s Interpretation for significant r values
Correlation: Pearson r
Correlation: Pearson r
Requirements for using Pearson r• The sample has been randomly selected from the population
• Measurement for both variables must be in the form of interval and/or ratio data
• The variables being measured must not depart significantly from normality
-variable data should take the shape of the normal curve if you measured the whole population
• The assumption of homoscedasticity is reasonable
-points are fairly equally distributed above & below the regression line
• The association is between X & Y is linear (not curvilinear)
-plot your data & make sure it takes an oval shape
Correlation: Pearson r
• Use Spearman rs when you can’t meet the requirements to use the Pearson
-when both sets of data are not interval and/or ratio
-when the data are skewed/non-normal distributions
-note: the Spearman rs (unike the Pearson r) is considered a non-parametric test
**ie. it does not make assumptions about normality of the population including the parameter mean or the parameter standard deviation
• Calculating Spearman rs (when you have ordinal data)
Formula:
Step 1: determine the rank of each subject on both variables
**if you have interval data (on one set) convert it to ordinal by ranking it
Step 2: Obtain the absolute difference, d, between each subject’s pair of ranks
Step 3: Square each difference, d2
Step 4: Calculate Σd2 by adding the squared differences
Step 5: Plug the values into the formula
Correlation: Spearman rs
• Case of ties
-if you have the same score for two or more subjects (see worksheet for example):
*add the ranks (that the scores are tied for) and divide by the number of tied scores
*give all the subjects that same rank
• Testing a hypothesis using correlation
-r refers to the sample correlation and ρs (rho) refers to the population correlation
Ho: ρs= 0 there is no correlation in the population
Ha: ρs≠ 0 there is a correlation in the population
• Critical Values (Table F)
-Use N (not df)
-if the calculated rs value is greater than or equal to the table r value then reject Ho
Correlation: Spearman rs
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