The Correlational Research Strategy

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Goal of correlational research stragegy

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examine and describe the association and relationships between variables

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purpose of correlational study

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establish that a relationship exist between variables and to describe the nature of the relationship

doesn't explain relationship or manipulate, control variables

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data for correlational study

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consist of two or more measurements, one for each variable being examined

ex. recording individuals iq and creativity for each person

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correlational research stratgery

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two or more variables are measured to obtain a set of scores for each individual. Measurements are then examined to identify any patterns of relationship that exist between variables and to measure the strength of the relationship

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individual

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refers to an single person but actually refers to single source

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scatter plot

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graph for correlations, show two scores for each individual appearing as one point

benefit: allows you to see the characteristics of the relationship between two variables

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correlation

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a statistical method used to measure and describe the relationship between 2 variables

A relationship exists when changes in one variable tend to be accompanied by consistent and predictable changes in the other variable

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correlation describes three characteristics of a relationship

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1. direction of the relationship
2.form of the relationship
3.consistency or strength of the relationship

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direction of the relationship

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positive relationship: variables change in same direction. Data points cluster around a line that slopes up to the right

negative relationship: negative values, data points change in opposite directions. On a scatter plot data plots that cluster around a line that slopes down to the right

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form of the relationship

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either linear or monotonic

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linear

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data points in a scatter tend to cluster around a straight line

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monotonic

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relationship is consistently one-directional either consistently positive or negative

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Pearson Correlation

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most commonly used. measures the degree and direction of the linear relation between two variables

- scores be numerical values from an interval or ratio scale of measurement.

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Spearman correlation

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measure monotinic relationship, used to measure the relationship between two ordinal variables
X and Y both consist of ranks
Measures the consistency of direction of the relationship between two variables

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degree or Consistency or strength of the relationship

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measured by numerical value obtained for correlation coefficient +1.00 or -1.00 indicates perfect consistent
0 no consistency

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Comparing correlational, experimental and differential research: experimental study

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seeks cause & effect relationship between two variables but measures only one. An experiment requires manipulation of one variable to create treatment condition and measurement of the 2nd variable to obtain scores within each condition. The researcher compares scores from each condition to determine if a cause exist

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Comparing correlational, experimental and differential research: correlation study

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seek to explore the existence of a relationship between two variables

researcher looks @ relationship between the set of scores

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Comparing correlational, experimental and differential research: differential research

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establishes the existence of a relationship by demonstrating difference between groups

uses one of the two variables to create groups of participants and then measures the second variable to obtain scores in each group. Seeks to determine a relationship between the groups whereas correlation looks at indivduals

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Applications of correlational strategy

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prediction
reliability and validity
evaluating theories

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predication

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establishing and describing the existence of a relationship , provide the basic information needed to make a prediction

ex. college adminstrators using SAT scores for college performance or parents Iq predicts children s iq

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predictor variable

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the first variable

ex. GRE

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criterion varable

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the second variable, the variable being explained or predicted

ex. Graduate school performance

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regression

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statistical techniques used for predicting one variable from another
goal is to find the equation that produces most accurate predictions of Y (the criterion) for each value of x (predictor value) for line of best fit

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reliability

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evaluates the consistency or stability of measurement

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validity

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evaluates the extent to which the measurement produce actually measures what it claims to be measuring

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concurrent validity

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demonstrated where a test correlates well with a measure that has previously been validated

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two additional factors to consider when interpreting strength of a relationship

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1. coefficient of determination
2.significance of correlation

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coefficient of determination

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r 2, most common measure for strength of a relationship compute by squaring the numerical value of the correlation
measures how much variability in one variable is predictable from its relationship with another variable
r=.30 would equall r2=.09

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Cohen's strength of relationship

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.10=small
.30=medium
.50=large

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significance of correlation

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want a large sample

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primary advantage

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researchers simply record what already or exist naturally

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correlation studies tend to have

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high external validity

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correlation studies tend to have low internal validity

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bc a correlational study does not produce clear and unambiguous explanation

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third variable problem

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a possible third unidentified variable is controlling two variables and is responsible for producing observed relation

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directionality problem

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changes in one varable tend to be accompanied by changes in another showing they are related but hard to determine which is the cause and effect

ex. watching sexual tv shows causes teens to have sex or do teens who have sex watch sexual tv shows

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multiple regression

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Uses more than one predictor variable to estimate the criterion
Y = a +b1X1 + b2X2 +…+bnXn

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Bivariate correlations

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-use two variables
-tests of association

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Pearson equation

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r= degree to which x and y vary together divided by degree to which x and y vary separately

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Interpretation of Pearson

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X could be causing Y
Y could be causing X
X and Y can be simultaneously causing each other.
A third variable (one that we haven't measured, or aren't aware of) could be causing both X and Y.

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Testing Hypotheses for Pearson
Null

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H0: ρ = 0 There is no population correlation

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Testing Hypotheses for Pearson
Alternative Hypothesis:

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H1: ρ ≠ 0 There is a real correlation

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Testing Hypotheses for Pearson
For direction

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Positive correlation (ρ > 0)
Negative correlation (ρ < 0)

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Testing Hypotheses for Pearson
Degrees of Freedom

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df = n — 2

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Point-biserial correlation

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One variable is dichotomous
The other variable consists of regular numerical scores (interval or ratio scale
related to the independent-measures t test

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Phi-coefficient

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both variables are dichotomous

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linear equation:
Y = a + bX
b

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b is called the slope of the line
determines the direction and degree to which the line is tilted
It determines how many points Y will change for every 1 unit change in X.
the slope is a measure of change in Y due to a unit change in X.

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linear equation:
Y = a + bX
a

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a is the intercept of the line
the value of Y when X is equal to 0
where the line intercepts the Y-axis

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Least Squares

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The distance between the actual data point (Y) and the predicted point on the line (Ŷ) is defined as Y – Ŷ.

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Error

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Unless the correlation is perfect (+1.00 or –1.00), there will be some error between the actual Y values and the predicted Y values. The larger the correlation is, the less the error will be.

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Hypotheses in Multiple Regression

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Is there an "overall" prediction of Y?
Considering both X1 and X2 together, do these variables predict the outcome?
This "amount of prediction" would be the entire middle shaded area (dots, solid, and the stripes).
Test specific hypotheses regarding each of the predictors alone:
Does X1 predict Y after controlling (removing) any effects of X2 (dots area)?
Does X2 predict Y after controlling (removing) any effects of X1 (stripes area)?

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Multiple Regression with 2 Predictor Variables

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In the same way that linear regression produces an equation that uses values of X to predict values of Y, multiple regression produces an equation that uses two different variables (X1 and X2) to predict values of Y

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multiple regression equation

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Ŷ= b1X1 + b2X2 + a

ability of the multiple regression equation to accurately predict the Y values is measured by first computing the proportion of the Y-score variability that is predicted by the regression equation and the proportion that is not predicted.

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Partial Correlation

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measures the relationship between two variables (X and Y) eliminating the influence of a third variable (Z).

used to reveal the real, underlying relationship between two variables when researchers suspect apparent relation may be distorted by a third variable.