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### 50 Cards in this Set

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 Describe what a correlation of -.9 would look like on a graph. Low Values of X go with high values of Y, Medium with Medium, and High with Low. The line is steep and has a negative slope. What is meant by Subgroup Differences and how can this produce a high value for r when no correlation exists? Subgroup differences are when the scores of 2 groups are plotted on a graph. The scores of one group are low and the scores of the other group are high BUT there is no correlation within each group. When the correlation coefficient is calculated, the high scores cause r to be higher and there is not a correlation between the variables. Pearson r cannot deal with non-linear data. How else can the data be viewed? -See if a function can be found that approximates the curve. Test for fit. -Divide variables into segments Why can't correlation values be added? Correlation values cannot be added because they are not linear. Square them or convert to Z-Scores Why is it important to examine a scatter plot and not judge the strength of a correlation by the value of r alone? The value of r does not guarantee a high correlation in the data. Make sure that a correlation of .5 is due to an actual trend in the data and not due to extreme scores, or random outliers. Make sure that a correlation of .5 or greater is not due to differences between groups. What is correlation and what values are possible for the Pearson Correlation Coefficient? Correlation is a measure of the relation between 2 or more variables. Perfect Positive Corr - r=1 Perfect Negative Corr - r=-1 Lack of Corr - r=0 What does a Pearson Correlation show? The two values are measured on interval scales and then compared to see the extent to which the 2 values are proportional to each other. What are some benefits of using the Pearson Correlation? -Measures extent to which the variables are proportional to each other. -Value does not depend on units of measurement. What does r, the Pearson Coefficient, represent? r represents the LINEAR relationship between the 2 variables. What factors can threaten the value of r and cause a correlation to be over or understated? -Outliers - value is squared and this changes the slope of the regression line and the value of r. -Correlations in groups that differ. Different groups may have a large mean difference. When compared, the value of r may be increased due to measurement differences betweent the groups, not because of a true relationship between the variables. -Deviations from LINEAR plots will increase the sum of the squared distances from the regression line. What is Reliability? Reliability tells if you can repeat the procedure and get the same score. It is a value that can only be estimated. What is True Score Theory? True Score Theory is a theory that says a measurement has 2 parts: True Level + Random Error X = T + Ex Why is True Score Theory important? -Says measures have an error component. -If a measure has no random error, it is accurate. Give some characteristics of Random Error Random error does not have consistent effects across the sample. Pushes scores up and down at random error. -Adds variability to the data but does not affect the mean of the group. Does Random Error affect the mean? How? Random error does not affect the size of the mean but it affects the variability around the mean. What is systematic error? Systematic error is caused by any factors that affect the measurement of the variable across the sample. Tends to be either positive or negative across the sample. A bias. Changes the mean. How can Measurement Error be reduced? -Pilot test instruments -Get feedback from participants to see if anything was very easy or very hard. -Train participants -Double check data, punch -Use multiple measures of the same construct to get better picture of whats going on. What is reliability? A measure is reliable if it gives the same result on various trials (as long as the subject is not changing). Repeatability, Consistency. What is variance? How is variance calculated? Variance is a measure of the distribution of the scores. Sum of the squared deviations from their mean divided by the number of scores. What is the equation for reliability and why can't it be precisely calculated? Variance of the true score/ variance of the measure Reliability cannot be calculated because What is Kurtosis? What is Leptokurtic? Kurtosis is the shape of the distribution. Leptokurtic is when all your scores go by in an instant. Explain why a correlation coefficient is not linear When data is plotted, 1 SD from the mean is rare, 2 SD's are very rare, and 3 SD's are extremely rare. The difference between .2 and .3 is small but the difference between .7 and .9 is great because of squaring. Explain why a high significance in correlation does not necessarily mean a high value. Points on a scatter plot have different influence. Points that are far from the average line influence the value of the correlation coefficient more than points that are closer to the line. Make sure a value of .5 is due to a trend in the data and not just extreme scores. How can scatter plot data be analyzed to insure that a .5 correlation is really a .5? 1. Look for mean differences between groups to make sure they are not inflating r. 2. Make sure outliers are not influencing the value of r. 3. Make sure a .5 is due to a trend in the data or a mechanism. What are weaknesses of Pearson Correlation? 1. Mean group differnces may inflate the value of r. Z Score everybody with the average of their group. There may be a high value for r but no correlation in each group. 2. Pearson does not work for non-linear relationships 3. Don't just look at number and think you know what is going on. Look at the data and see how you got there. Why must correlations be converted to Z scores before averaging? Give higher weight to bigger correlation. What are Venn Diagrams used for? Show extent to which 2 variables are correlated. No overlap = 0 Correlation Complete Overlap = 100% correlation. T Observed = T true + T error What does error do to a correlation and why? Brings it down. Even if reliablility of Test is 1, multiplying by sqr 1 = best value you can get. Observed correlations are always _______ than the true score. Less than r = true 1 * true 2 r obs 1 * r obs 2 divided by sqr rlabilty 1 * sqr rlb 2 What is needed to calculate true score? True score is hypothetical and can't be measured but if you have: 1. correlation between the tests and 2. the reliabilities of the tests What 2 things can make a test more reliable? 1. Make the test longer, a longer test is more reliable BECAUSE error averages out. Therefore behavior becomes more reliable. 2. Are items in the test highly correlated with each other? If so, there is greater chance that they are measuring the same thing. How can it be proven that the maximum value for Pearson r is always 1? Let x = y for every subject. Top part of equation becomes the mean product of deviation scores, so does bottom, and fraction = 1.0 What 2 aspects are included in a measure? R + V Reliability + Validity. R = can you measure again and get same results. V = can you interpret the measure to have a certain meaning. What 2 things make up a person's score on a measure? True Score + Error Component T obs = True + Error What are characteristics of a true score? Of Error? Stays the same unless you change. Erro is RANDOM every time you are measured. What is the Reliability of a test? The reliability of a test is the extent to which DIVERSITY among the observed scores reflects the DIVERSITY in the subjects True scores. What 2 factors determine the reliability of a test? 1. Test lenght. Longer = more reliable. 2. How highly correlated the items are. How does low reliability affect a correlation? Lowers it: if r = .7 and reliabilty is .5: .7 * .5 = .35, an underestimation How can Reliability be defined Repeatability, can only be estimated. You can repeat the same procedure and get the same score. What is the concept behind True Score Theory? That an observed score is: Observed score = True ability + Random Error Why is True Score Theory Important? Measurement has an error component. Shows that a measure that has no error is Reliable. How does random error affect a distribution? What is systematic error? The average stays the same, but the variability around the average changes. Systematic error is bias. Noise, etc. How can error be reduced? 1. Ask participants if anything was extremely easy or difficult. 2. Train people that are collecting data. 3. Double punch data entry 4. Use several measures of the same construct When a measure gives the same result over and over, it is _____, as long as what is being measured is not changing. Reliable Why can't reliablity be calculated? Because we can't calculate the VARIANCE of the True scores. What does the Theory of Reliability say about calculating reliabilty? Reliabilty cannot be calculated exactly. It can only be estimated. If a measure is reliable but not valid ... You get the same answer over and over, but its the wrong one. If your measure is neither reliable nor valid ... You miss the target and are spread out all over the place.