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Nussbaum D (52)
Chapter 10

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Nussbaum D

CHAPTER 10 Does Spending Money On Others Promote Happiness? Participants randomly assigned to:  Money condition($5 or $20)  Spending condition (self or others) 2 x 2 between-subjects factorial design Statistical Approach Descriptive statistics: used to describe the variables in a study, both one at a time and in terms of their relations to each other.  Age, gender, socioeconomic status Inferential statistics: used to estimate characteristics of a population from those that were found in a random sample of that population.  Can also be used to test hypothesis about the relationships between variables Level of Measurement - review Nominal: categorical level of measurement Interval: numbers indicating a variable’s values represent fixed measurement units but have no absolute, or fixed, zero point Ratio: numbers indicating a variable’s values represent fixed measuring units and have an absolute zero point Frequency of Distributions Def.: shows the number of cases and/or the percentage of cases who receive each possible score on a variable Often precedes the formal statistical analysis May group the values if:  There are more than 15-20/ category  It would clarify the distribution Guidelines for combining values in a frequency distribution:  Categories should be logically defensible and preserve the distribution’s shape  Categories should be mutually exclusive and exhaustive so that every case should be classifiable in one and only one category Graphing Bar charts  Bars separated by spaces  Good for nominal data Histograms  Displays a frequency distribution of a quantitative variable Avoiding Misleading Graphs Begin the graph of a quantitative variable at 0 on both axes Always use bars of equal width The two axes should be of approximately equal length Avoid “chart junk”  Stupid lines, cross-hatching, too many marks Descriptive Statistics Whatever display is used, is important to preserve shape of graph. This means thinking of central tendency, variability, and skewness.  Variability: the extent to which cases are spread out through the distribution or clustered in just one location  Skewness: extent to which cases are clustered more at one or other end of the distribution of a quantitative variable rather than in a symmetric pattern around its center. o Positive  Right skew, tapering off in positive direction o Negative  Left skew, tapering off in negative direction Measures of Central Tendency Central tendency: most common value or the value around which cases tend to center Choosing the appropriate measure of central tendency, the researcher needs to consider level of measurement, skewness of the distribution of the variable, and the purpose for which the statistic is used. Mode (probability average)  Most frequent score  May be more than one  May fall far from the main clustering of cases in a distribution Mode is used less often because it can give misleading impression of a distribution central tendency.  This can occur when a distribution is bimodal (has two or more categories with an equal number of cases and with more cases than any other categories) rather than unimodal (single mode). This means that there is no single mode.  Mode can fall far from the main clustering of cases in a distribution. Gives misleading to say that the central tendency was the mode. Median (position average)  Point that divides the distribution in half  Cannot be used at the nominal level  Adding the frequencies of the two middle values and dividing by two. Mean (arithmetic average)  Sum numbers and divide by N  Cannot be used at the nominal level (and sometimes not at the ordinal level) Mean vs. Median  Should consider the purpose of the statistic  Median often makes more sense if the scale is at the Ordinal level  Median is better for skewed distributions  Cannot use either of these for values at the nominal level, as the different attributes of a variable cannot be ordered as higher or lower  Mean is most often used for quantitative variables Variability Variance: Average squared deviation of each case from the mean Range  High score – low score  Drastically influenced by one high or low score  Range = highest value – lowest value + 1 Standard Deviation: Square root of the variance Sampling Distributions Distribution of statistics representing all possible samples drawn from a population of a set size  Mean is the same as the population mean  Standard error of the mean: degree to which the means of the samples vary from the population mean Inferential Statistics Confidence that the mean of a random sample from a population is within a certain range of the population mean Calculating confidence limits: 1. Calculate the standard error a. b. N= n-1 2. Decide on a degree of confidence – this can be 95%, 99%, or 99.9%. a. Usually, 95% is used 3. Multiply the standard error by 1.96 4. Add and subtract the value in step 3 from the sample mean Inferential statistics (Cont.) Can be used to estimate a population parameter from a sample statistic Can also be used to test a hypothesis Two of the most common hypothesis tests:  t-test  F-test Hypothesis Testing
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