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Chapter 5 Description of Behavior Through Numerical Representation @ 2012 Wadsworth, Cengage Learning Topics 1. 2. 3. 4. Measurement Scales of Measurement Measurement and Statistics Pictorial Description of Frequency Information 5. Descriptive Statistics @ 2012 Wadsworth, Cengage Learning Topics (cont’d.) 6. 7. 8. 9. Pictorial Presentations of Numerical Data Transforming Data Standard Scores Measure of Association @ 2012 Wadsworth, Cengage Learning Measurement @ 2012 Wadsworth, Cengage Learning Measurement • “What can we measure?” • “What do the measurements mean?” • Four properties: – Identity – Magnitude – Equal intervals – Absolute zero @ 2012 Wadsworth, Cengage Learning Scales of Measurement @ 2012 Wadsworth, Cengage Learning Scales of Measurement • Nominal measurement – Occurs when people are placed into different categories – Example: classify research participants as men or women – Differences between categories are of kind @ 2012 Wadsworth, Cengage Learning Scales of Measurement (cont’d.) • Ordinal measurement – A single continuum underlies a particular classification system – Example: pop-music charts – Represents some degree of quantitative difference – Transforms information expressed in one form to that expressed in another @ 2012 Wadsworth, Cengage Learning Scales of Measurement (cont’d.) • Interval measurement – Requires that: • Scale values are related by a single underlying quantitative dimension • There are equal intervals between consecutive scale values – Example: household thermometer @ 2012 Wadsworth, Cengage Learning Scales of Measurement (cont’d.) • Ratio measurement – Requires that: • Scores are related by a single quantitative dimension • Scores are separated by equal intervals • There is an absolute zero – Example: weight, length • Scales of measurement are related to: – How a particular concept is being measured – The questions being asked @ 2012 Wadsworth, Cengage Learning Measurement and Statistics @ 2012 Wadsworth, Cengage Learning Measurement and Statistics • No statistical reason exists for limiting a particular scale of measurement to a particular statistical procedure • Your statistics do not know and do not care where your numbers come from @ 2012 Wadsworth, Cengage Learning Pictorial Description of Frequency Information @ 2012 Wadsworth, Cengage Learning Pictorial Description of Frequency Information Table 5.2 @ 2012 Wadsworth, Cengage Learning Pictorial Description of Frequency Information (cont’d.) Figure 5.1 Bar graph of dream data @ 2012 Wadsworth, Cengage Learning Pictorial Description of Frequency Information (cont’d.) Figure 5.2 Frequency polygon of dream data @ 2012 Wadsworth, Cengage Learning Figure 5.3 Four types of frequency distributions: (a) normal, (b) bimodal, (c) positively skewed, and (d) negatively skewed @ 2012 Wadsworth, Cengage Learning Descriptive Statistics @ 2012 Wadsworth, Cengage Learning Measures of Central Tendency • Mean – Arithmetic average of a set of scores • Median – List scores in order of magnitude; the median is the middle score or – In the case of an even number of scores, the score halfway between the two middle scores • Mode – Most frequently occurring score @ 2012 Wadsworth, Cengage Learning Figure 5.4 Mean, median, and mode of (a) a normal distribution and (b) a skewed distribution @ 2012 Wadsworth, Cengage Learning Measures of Variability • Attempts to indicate how spread out the scores are • Range: reflects the difference between the largest and smallest scores in a set of data • Variance: average of the squared deviations from the mean • To determine variance: – First calculate the sum of squares (SS) @ 2012 Wadsworth, Cengage Learning Measures of Variability (cont’d.) • Deviation method: sum of squares is equal to the sum of the squared deviation scores • Second way to calculate the sum of squares: computational formula @ 2012 Wadsworth, Cengage Learning Measures of Variability (cont’d.) • Formula for variance: • Square root of the variance: standard deviation (SD) @ 2012 Wadsworth, Cengage Learning Pictorial Presentations of Numerical Data @ 2012 Wadsworth, Cengage Learning Pictorial Presentation of Numerical Data Figure 5.6 Effects of room temperature on response rates in rats @ 2012 Wadsworth, Cengage Learning Pictorial Presentation of Numerical Data (cont’d.) Figure 5.7 Effects of different forms of therapy @ 2012 Wadsworth, Cengage Learning Transforming Data @ 2012 Wadsworth, Cengage Learning Transforming Data • Transformations are important – Used to compare data collected using one scale with those collected using another • A statement is meaningful if: – The truth or falsity of the statement remains unchanged when one scale is replaced by another @ 2012 Wadsworth, Cengage Learning Standard Scores @ 2012 Wadsworth, Cengage Learning Standard Scores • Formula for z score: • Two important characteristics of the z score: – If we were to transform a set of data to z scores, the mean of these scores would equal 0 – The standard deviation of this set of z scores would equal 1 @ 2012 Wadsworth, Cengage Learning Measure of Association @ 2012 Wadsworth, Cengage Learning Figure 5.10 Scatter diagrams showing various relationships that differ in degree and direction @ 2012 Wadsworth, Cengage Learning Measure of Association (cont’d.) • Formula for the Pearson product moment correlation coefficient (r): • Correlations: – Have to do with associations between two measures – Tell nothing about the causal relationship between the two variables @ 2012 Wadsworth, Cengage Learning Measure of Association (cont’d.) • When you square the correlation coefficient (r2) and multiply this number by 100 – You have the amount of the variance in one measure due to the other measure • Regression: – Mathematical way to use data – Estimates how well we can predict that a change in one variable will lead to a change in another variable @ 2012 Wadsworth, Cengage Learning Summary • Three important measures of central tendency are the mean, median, and mode • Some scores may be transformed from one scale to another • Variability, or dispersion, is related to how spread out a set of scores is • A correlation aids us in understanding how two sets of scores are related @ 2012 Wadsworth, Cengage Learning