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research Ch. 11

correlational designs

TermDefinition
Correlation a statistical procedure that is used to measure and describe a relationship between two variables. In general, these variables are continuous—interval or ratio scales
3 Characteristics of a Correlation 1. The direction of the relationship 2. The Form of the Relation 3. The Degree of the Relationship
The direction of the relationship 2 basic categories -Positive correlation: as the value of one variable increases, the value of the other variable also increases -Negative Correlation:as the value of one variable increases, the value of the other variable decreases relationship is ind
The Form of the Relation The most common form is linear- A relationship described by a straight line. A perfect linear relationship (r = +1.00 or -1.00) is when all the data point lie on a straight line in a scatter plot. Other forms include curvilinear
The Degree of the Relationship A perfect relationship is +1.00 or -1.00; the lack of a relationship is r = .00
The 4 Major Uses of Correlations Prediction Validity Reliability Theory Verification
Prediciton -If two variables are known to be related in a systematic way, then we can use one of the variables to predict the other variable. E.g., If we assume that SAT scores are related to college GPA, I can predict a student’s GPA in college based on their SAT
Validity -How does a psychologist know if a new test measures what it suppose to measure? Developing a new depression test and correlating it with the Hamilton Depression Rating Scale. The MTMM is a correlation matrix used to prove construct validity
Reliability A measurement procedure is considered reliable to the extent it produces stable, consist measurements. In other words, the same individuals should score very similar scores under similar conditions. ex: MTMM
Theory Verification -Many psychological therapies make specific predictions about the relationship between two variables Ex: Behavioral Therapy suggests that depression is sustained because less events that are pleasant to the depressed patient is experienced
Issues in Interpreting Correlations -does not prove cause-effect -affected by range of scores -measurement error -outliers -not to be interpreted as proportion of "variance explained" -linear transformations -bivariate normal distribution
Correlation simple describes a relationship between 2 variables It does NOT explain why the 2 variables are related. It cannot prove a cause-and-effect relationship. This is true because there is no systematic manipulation of a variable
Ceiling Effect An undesirable measurement outcome occurring when the dependent measure puts an artificially “low ceiling” on how high a participant may score.
Floor Effect The dependent measure artificially restricts how low scores can be. Example: A problem-solving test that is so difficult, no one gets any of the questions right
Restriction of Range To observe a sizeable correlation between two variables, both must be allowed to vary widely
Coefficient of Determination It measures the proportion of variability in r^2; one variable that can be determined from the relationship with the other variable
Linear transformations It does not matter if the scores of either variables are transformed in to standard scores or added or multiplied by a constant, the correlation between the two variables will remain the same
Bivariate normal distribution -the frequency of the correlations between 2 variables X and Y. -sampling distribution is 3d and will be normally distributed as sample size increases -the distribution of the frequency of scores looks like a pitcher’s mound in a baseball field
Simple Regression -Pearson correlation measures the linear relationship between two continuous variables. -The data presented above on the scatter plot graph shows a good, but not perfect, linear relationship. -A line is drawn through the middle of the data points
This line called the Regression Line serves 3 purposes 1.It helps describe the relationship between the two variables. 2.It identifies the center or ”central tendency” of the relation. 3.The line can be used for prediction
Regression line the straight line that best describes the linear relationship between two variables
Homoscedasticity -is assumed when sample size is large. cannot be assumed when the sample size is small -homoscedasticity= variance of Y scores for each value of X -equal spread of data points from regression line for all values of x
Standard Error of Measure -provides a measure of the standard distance between the regression line and the actual data points -Conceptually the SE of the estimate is like the standard deviation -accuracy is determined by standard error measurement -review class notes on SE
Regression to the Mean -In pre&posttest study,the sample's posttest mean is closer to the posttest population mean than their pretest mean was to the pretest population mean -occurs when you have a nonrandom sample from a pop. and 2 measures that are imperfectly correlated
Multiple Regression -the weights for this line are selectged ont he basis of the least squares criterion where the sum of the squared residuals is at a minimum and the sum of squares for the regression is at a maximum -y-bx1+bx2+bx3...bxi+a -ex: venn diagram exercise
Factor analysis a statistical procedure in which the correlations between responses (variables) to questionnaires or other measures are used to discover common underlying factors; those variables that are highly correlated are “grouped” together to make a factor
Factor a group of interrelated variables
Factor loading the correlation between the variable and the factor; they range from -1 to +1. Normally, a variable is considered to contribute meaningfully to a factor with a loading of at least +0.30
Some Uses of Factor Analysis -To establish patterns between Interdependent or interrelated variables or items -Parsimony or data reduction -Structure -Classification or description -Hypothesis testing -Exploration -Theory
To establish patterns between Interdependent or interrelated variables or items -Factor analysis may be used to untangle the linear relationships into their separate patterns within items of a measure or groups of measures. -Each pattern will appear as a factor delineating a distinct cluster of interrelated data
Parsimony or data reduction -Factor analysis can be useful for reducing a mass of information to an economical description
Structure -Factor analysis may be employed to discover the basic structure of a domain. For instance, what makes up the factor social anxiety?
Classification or description -Factor analysis can be used to group interdependent variables into descriptive categories e.g ideology, revolution, liberal voting, and authoritarianism. -It can be used to classify nation profiles into types with similar characteristics or behavior
Hypothesis testing -hyotheses regarding dimensions of attitude, personality, group, etc.; factor analyses can be used to test for empirical existence -dimensions can be postulated in advance and statistical tests of signif. can be applied to factor analysis
Exploration -unknown domain explored through factor analy. -Factor analy. fulfills enables the scientist to untangle interrelationships, to separate different sources of variation, and to partial out or control for undesirable influences on the variables of concern
Theory • Analytic framework of social theories or models can be built from the geometric or algebraic structure of factor analysis
Created by: rperales24
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