Stats - Statistics 350 Notes Final Exam Study Guide Chapter...

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Statistics 350 Notes Final Exam Study Guide Chapter 2 : Variable – a characteristic that differs from one individual to the next Categorical variable – places an individual into one of several groups or categories; if it has ordered categories, it is called an ordinal variable (seat location, current smoker, soft drink size, etc.) Quantitative variable – numerical values (age, number of CDs owned, times spent talking on cell phone, etc.) Explanatory vs. response variables – which causes the other? Shapes: bell-shaped, uniform, skewed, unimodal, bimodal Skewed right = tail is on right, median is less than mean Skewed left = tail is on left, mean is less than median Location (center, average): approximate middle value Spread (variability): standard deviation, range Outliers – points that are not consistent with the bulk of the data Mean – the numerical average value (mean of a sample = x-bar) The mean is sensitive to extreme observations The median is resistant to extreme observations Median = 50 th percentile, Q 2 First quartile = 25 th percentile, Q 1 Third quartile = 75 th percentile, Q 3 Interquartile range (IQR *middle 50% of data) = Q 3 - Q 1 Check for outliers by using the 1.5*IQR rule (Q 3 /Q 1 – 1.5*IQR) Boxplots: cannot confirm shape Normal Distributions Standard deviation – the measure of the spread of the observations from the mean (roughly, the average distance the observations fall from the mean) Variance = s 2 , standard deviation = s Interpretation of the standard deviation: The weights of small orders of French fries are roughly 6 grams away from their mean weight of 73.6 grams, on average. Standard deviation is sensitive to outliers and extreme observations
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Empirical Rule – For bell-shaped curves, approximately… 68% of the values fall within 1 standard deviation from the mean in either direction 95% of the values fall within 2 standard deviations from the mean in either direction 99.7% of the values fall within 3 standard deviations from the mean in either direction Standardized scores (z-score) – the distance between the observed value and the mean, measured in terms of the number of standard deviations Z-score = (observed value – mean) / standard deviation Chapter 3 : Selection bias – if the method for selecting the participants produces a sample that does not represent the population of interest Nonresponse bias – when a representative sample is chosen for a survey, but a subset cannot be contacted or does not respond Response bias – when participants respond differently from how they truly feel (wording of the question, the way an interviewer behaves, etc. might lead an individual to provide false information) Margin of error – the measure of accuracy in sample surveys (how close that proportion comes to t he truth for the entire population) Chapter 4 Observational studies – researches simply observe or question the participants about opinions, behaviors, or outcomes
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