METHODS 2 CH 2 Descriptive Statistics o Variable something that can vary or change o Dependent variable something we measure o Data a collection of measurements o Statistics summary descriptions of data i e mean medium range Used to describe or summarize sets of data to make them more understandable o measures of central tendency Specify the location of a distribution mean median mode o measures of variability Specify the spread or dispersion of a distribution range variance standard deviation o measures of association Specify the relationship between or among variables correlation coefficient Distributions Measures of Central Tendency o What is the average family income above o Mean the arithmetic average o Median the center score o Mode the score that occurs the most Distributions Measures of Variability o Range the difference between the highest and lowest score in a set of data o Variance Average squared deviation of a score from the mean o Standard deviation square root of the variance reflects the average distance between every score and the mean in the unit of the mean Distributions Positive Skew see PowerPoint slide Distributions Negative Skew see PowerPoint slide Distributions Bimodal Distribution see PowerPoint slide Distributions Normal Distribution below Distributions Normal Distribution same location difference in spread or variability below Correlation Coefficient o Often we measure more than one variable o Grade point and SAT score o Are they related o Correlation statistic is a way to find out o Measures whether two variables change in a related way Can be positive strongest is r 1 00 see PowerPoint slide Negative strongest is r 1 00 see PowerPoint slide Or not related r 0 00 Inferential Statistics o Descriptive statistics summarize a data set o We often want to go beyond the data o Is the world at large like my sample o Are my descriptive statistics misleading o o Results Schachter 1959 Inferential statistics give probability that the sample is like the world at large Wanted to Wait with Others Didn t Care Wanted to Wait Alone Group Total N 20 10 30 62 5 33 3 48 4 N 9 18 27 28 1 60 0 43 5 High Anxiety Low Anxiety Response Total Adapted from Schachter S 1959 The psychology of affiliation Experimental studies of the sources of gregariousness Stanford CA Stanford University Press 9 4 6 7 8 1 N 3 2 5 N 32 30 62 Inferential Statistics continued How likely is it that these results are due to chance alone Conventionally it is generally agreed that if the pattern of results are such that it would occur less than five percent of the time given a null pattern no difference between the groups then it is considered to be unlikely that the results are due to chance Note If the null pattern were the true pattern and our results were such that they occurred only less than 5 we would have made an error in our inference according to the conventional process A test of proportions suggests that people experiencing higher levels of anxiety are significantly more likely to want to be together with other people Fisher s Exact p 0 03 Note Schachter scored his ordinal dependent measure as if it were on an interval scale but his conclusions were essentially the same as what the proportion test shows o Types of Error in Inference TYPE I Error o TYPE II Error 1 The TRUE pattern is null there is in the world no real difference 2 between groups If we find that our results suggest that we should infer a difference between groups i e the pattern of results appears to occur less than 5 of time assuming a null pattern we have made a Type I error 3 We assumed the correct distribution but are results suggested that it was the wrong distribution Our assumption was correct our conclusion was wrong 1 The TRUE pattern is not null there is in the world a real difference 2 between groups If we find that our results suggest that we should infer no difference between groups when one actually exists i e the pattern of results appears to occur greater than 5 of time assuming a null pattern we have made a Type II error 3 We assumed the incorrect distribution i e the null distribution but our results suggested that the null distribution was the correct distribution Our assumption was incorrect and our conclusion was wrong o Controlling for Error in Inference Type I error is set by the researcher before analysis again this is conventionally set at 5 e g 0 05 Type II error depends on at least four factors 1 the larger the Type I error the lower the Type II error 2 Magnitude of the difference between groups Effect Size or 2 the larger the effect size the smaller the Type II error 3 The number of observations N the more observations in a study the smaller the Type II error Note however that this will also increase the likelihood of making a Type I error if the effect size is small 4 Variability in the data This will increase error in general Power of a statistical inference test 1 thus increases with a 2 N and decreases with increasing error variability Measurement and or people Measurement Errors Sources of Bias o Reliability a measure is reliable to the extent that it is consistent across time situation o Validity a measure is valid to the extent that it measures what it intends to measure o Why is inference based on probability instead of certainty o Data can be misleading because of variability o Data can be misleading because of bias o Biased sample when the members of a sample differ in a systematic way from the larger population the researcher is interested in o Example interested in all voters contact by telephone biased sample lower economic groups may not own telephones researcher has expectations that influence measurements subject knows design and tries to produce expected result o Observer expectancy effect o Subject expectancy effect o Blinding conditions minimize expectancy by removing knowledge about experimental o Single blind study when subjects are kept uninformed as to the treatment they are o Double blind study when both subjects and experimenter are kept uninformed about aspects of the study that could lead to differential expectations Blinding receiving Ethical Issues o Right to privacy o Informed consent use of deception o Animal rights Is there justification for discomfort or harm a research procedure may produce o APA publishes ethical guidelines