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Chapter 7: Correlational Research
1.1 Define correlational research. 
Correlational research involves collecting data to determine whether and to what degree a relationship exists between two or more variables. The degree of relationship is expressed as a correlation coefficient

Chapter 7: Correlational Research
1.2 State two purposes of correlational research. 
Purpose:
1. Determine relationships 2. Make predictions 
Chapter 7: Correlational Research
1.3 Understand the limitation of correlational research with regard to cause and effect. 
Limitation
Cannot indicate cause and effect. The fact that there is a relationship between variables does not imply that one is the cause of the other. Correlations do not describe causal relationships. You cannot prove that one variable causes another with correlational data. 
Chapter 7: Correlational Research
2.1 Explain the basis for problem selection in correlational research. 
Problem selection
Correlational studies may be designed either to determine which variables of a list of likely candidates are related or to test hypotheses regarding expected relationships. The variables to be correlated should be selected on the basis of some rationale suggested by theory or expereince. Variables to be correlated are selected on the basis of some rationale Math attitudes and math achievement Teachers’ sense of efficacy and their effectiveness Increases the ability to meaningfully interpret results 
Chapter 7: Correlational Research
2.2 Describe an acceptable sample size in correlational research. 
A common minimally accepted sample size for a correlational study is 30 participants.

Chapter 7: Correlational Research
2.3 Explain the relationship of instrument validity and reliability with regard to sample size in correlational research. 
Instruments must be valid and reliable
Higher validity and reliability requires smaller samples Lower validity and reliability requires larger samples 
Chapter 7: Correlational Research
3.1 Define the term correlation coefficient. 
A correlation coefficient is a decimal number between +1.00 and 1.00. It describes both the size and direction of the relationship between two variables. If the correlation coefficient is near .00, the variables are not related.

Chapter 7: Correlational Research
3.2 Identify the possible magnitude of a correlation coefficient. 
Size/magnitude
Ranges from 0.00 – 1.00 
Chapter 7: Correlational Research
3.3 Identify the two possible directions of a correlation coefficient and explain the meaning of each. 
A correlation coefficient near +1.00 indicates that the variables ae highly and positively related. An increase on one variable is associated with an increase on the other.
If the correlation coefficient is near 1.00, the variables are highly and negatively or inversely related. An increase on one variable is associated with a decrease on the other variable. 
Chapter 7: Correlational Research
3.4 Define and describe a scatterplot. 

Chapter 7: Correlational Research
3.5 State the range of values used to interpret low, moderate, and high correlation coefficients. 
General rule
Less than .35 is a low correlation Between .36 and .65 is a moderate correlation Above .66 is a high correlation Predictions Between .60 and .70 are adequate for group predictions Above .80 is adequate for individual predictions Interpreting the size and direction of correlations using the general rule +.95 is a strong positive correlation +.50 is a moderate positive correlation +.20 is a low positive correlation .26 is a low negative correlation .49 is a moderate negative correlation .95 is a strong negative correlation 
Chapter 7: Correlational Research
3.6 Define common variance. 
Definition
The extent to which variables vary in a systematic manner Interpreted as the percentage of variance in the criterion variable explained by the predictor variable 
Chapter 7: Correlational Research
3.7 State the formula for calculating common variance. 
The squared correlation coefficient  r2
Examples If r = .50 then r2 = .25 25% of the variance in the criterion can be explained by the predictor If r = .70 then r2 = .49 49% of the variance in the criterion can be explained by the predictor 
Chapter 7: Correlational Research
4.1 Define statistical significance in the context of correlation. 
Statistical significance refers to whether the obtained coeffivient is really different from zero and reflects a true relationship, not a chance relationship. To determine how large your correlation coefficient needs to be, to be statistically significant, you find the value in a table from which you can choose a level of significance and the size of your sample.

Chapter 7: Correlational Research
4.2 Explain how sample size affects statistical significance of a correlation coefficient. 
For a given level of significance, the smaller the sample size, the larger the coefficient requried. For a given sample size, the value of the correlation coefficient needed for significance increases as the level of confidence increases.

Chapter 7: Correlational Research
4.3 Define significance level and identify three commonly accepted levels of significance. 
Three common levels of significance
.01 (1 chance out of 100) .05 (5 chances out of 100) .10 (10 chances out of 100) 
Chapter 7: Correlational Research
4.4 Explain how a small correlation coefficient can be statistically significant. 
Small correlation coefficients can be statistically significant even though they have little practical significance
+.20 Statistically significant at the .05 level if the sample is about 100 Little or no practical significance because it is very low and predicts only .04 of the variation in the criterion scores .30 Statistically significant at the .05 level if the sample is about 40 Little or no practical significance because it is low and predicts only .09 of the variation in the criterion scores 
Chapter 7: Correlational Research
5.1 Describe the general purpose of a relationship study and differentiate it from correlational research studies. 
A relationship study is conducted to gain insight into the variables, of factors, that are related to a complex variable, such as academic achievement, motivation, or selfconcept. Such studies give direction to subsequent causalcomparative and expereimental studies.

Chapter 7: Correlational Research
5.2 Identify two major purposes of relationship studies. 
Suggest subsequent interest in establishing cause and effect between variables found to be related
Control for variables related to the dependent variable in experimental studies 
Chapter 7: Correlational Research
6.1 Identify and briefly describe the steps involved in conducting a relationship study. 
1. Identify a set of variables
Limit to those variables logically related to the criterion Avoid the shotgun approach Possibility of erroneous relationships Issues related to determining statistical significance 2. Identify a population and select a sample 3. Identify appropriate instruments for measuring each variable 4. Collect data for each instrument from each subject 5. Compute the appropriate correlation coefficient 
Chapter 7: Correlational Research
6.2 Explain the problem in calculating a large number of correlation coefficients in a single study. 
The more correlation coefficients that are computed at one time, the more likely it is that some wrong conclusions about the existence of a relationship will be reached. Thus, a smaller number of carefully selected variables is much preferred to a larger number of carelessly selected variables

Chapter 7: Correlational Research
7.1 State the type of correlation coefficient used to correlate continuous data. 
Pearson r  continuous predictor and criterion variables
Variable 1; Continuous data (i.e., ratio or interval) Variable 2: Continuous data (i.e., ratio or interval) Most common correlation Math attitude and math achievement 
Chapter 7: Correlational Research
7.2 State the type(s) of correlation coefficient used to correlate rank or ordinal data. 
Spearman rho – ranked or ordinal predictor and criterion variables
Rank in class and rank on a final exam 
Chapter 7: Correlational Research
7.3 State the type(s) of correlation coefficient used to correlate dichotomous data. 
Phi coefficient – dichotomous predictor and criterion variables
Gender and pass/fail status on a high stakes test 
Chapter 7: Correlational Research
8.1 Describe the difference between a linear and curvilinear relationship. 
Most correlational techniques are concerned with investigating linear relationships. A linear relationship, one in which an increase (or decrease) in one variable is associated with a corresponding increase (or decrease) in another variable. Plotting the socres of two variables that have a linear relationship results in a straight line. If a relationship is instead curvilinear, an increase in one variable is associated with a corresponding increase in another variable to a point, at which point further increase in the first variable results in a corresponding decrease in the other variable (or vice versa)

Chapter 7: Correlational Research
8.2 Give an example of two variables that might show a curvilinear relationship. 
Age and athletic ability
Anxiety and achievement 
Chapter 7: Correlational Research
8.3 State the type of correlation coefficient calculated when data are expected to relate in a curvilinear manner. 
1

Chapter 7: Correlational Research
8.4 Draw scatterplots of a strong positive relationship, a strong negative relationship, no relationship, and a curvilinear relationship. 
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Chapter 7: Correlational Research
9.1 Describe the reason for wanting to examine correlations for subgroups and identify the major problem with not doing so. 
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Chapter 7: Correlational Research
9.2 Define attenuation and explain how attenuation affects correlation coefficients. 
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Chapter 7: Correlational Research
9.3 Explain how low variability in a set of scores affects correlation coefficients. 
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Chapter 7: Correlational Research
10.1 Define the term predictor variable. 
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Chapter 7: Correlational Research
10.2 Define the term criterion variable. 
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Chapter 7: Correlational Research
10.3 Describe a situation in which there is a predictive relationship between two or more variables. 
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Chapter 7: Correlational Research
11.1 Identify three purposes of prediction studies. 
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Chapter 7: Correlational Research
11.2 Differentiate between correlation, relationship, and predictive studies. 
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Chapter 7: Correlational Research
11.3 Explain how shrinkage affects prediction equations. 
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Chapter 7: Correlational Research
11.4 Differentiate single and multiple predictor studies. 
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Chapter 7: Correlational Research
11.5 Identify three factors that affect the accuracy of prediction. 
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Chapter 7: Correlational Research
11.6 Define the coefficient of determination. 
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Chapter 7: Correlational Research
12.1 Explain the major difference between data collection in a relationship and predictive study. 
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Chapter 7: Correlational Research
13.1 Define path analysis. 
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Chapter 7: Correlational Research
13.2 State the purpose of discriminant function analysis. 
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13.3 Explain when you would use canonical correlation. 
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Chapter 7: Correlational Research
13.4 Explain the purpose of factor analysis. 
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