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BHS 204-01 Methods in Behavioral Sciences I April 21, 2003 Chapter 4 & 5 (Stanovich) Demonstrating Causation Figure 4.5. (p. 93) Two different distributions with the same range and mean but different dispersions of scores. Standard Deviation Average distance of scores from the mean. Calculated by taking the square root of the variance. The variance scores were squared so that the average of positive and negative distances from the mean could be combined. Taking the square root reverses this squaring and gives us a number expressed in our original units of measurement (instead of squared units). Graphing Data Line graph – used for ordinal, interval, ratio data. Independent variable on the x-axis Dependent variable on the y-axis Bar graph – used for categorical data. Figure 4.6. (p. 97) Effects of room temperature on response rates in rats. Figure 4.7. (p. 97) Effects of different forms of therapy. Transforming Data Sometimes it is useful to change the form of the data in some way: Converting F to C temperatures. Converting inches to centimeters. Transformation let you compare results across studies. Transformation must preserve the meaning of the data set and the relationships within it. Standard Scores One way to transform data in order to compare two data sets is to express all scores in terms of the distance from the mean. This is called a z-score. z = (score – mean) / standard deviation z-scores can be transformed so that all scores are positive: This is called a T-score T = 10 x z + 50 Measures of Association Scatter plot – used to show how two dependent variables vary in relation to each other. One variable on x-axis, the other on y-axis. Correlation – a statistics that describes the relationship between two variables – how they vary together. Correlations range from -1 to 1. Figure 4.9. (p. 102) Scatter diagram showing negative relationship between two measures. Figure 4.10. (p. 103) Scatter diagrams showing various relationships that differ in degree and direction. The Problem with Testimonials The Placebo effect The “vividness” problem. The P.T. Barnum effect. Correlation and Causation The “third variable” problem. The directionality problem. Selection bias.