Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Review Mean—arithmetic average, sum of all scores divided by the number of scores Median—balance point of the data, exact middle of the distribution, 50th percentile Mode—highest frequency, can be more than one Find the mean, median, mode Review Review Find the mean, median, mode Mean=sum of all scores(∑fX) /number of scores(N) Review Find the mean, median, mode Mean=sum of all scores(∑fX) /number of scores(N) Median=middle point (N-1/2)th position Review Find the mean, median, mode Mean=sum of all scores(∑fX) /number of scores(N) Median=middle point (N-1/2)th position Mode=greatest f Major Points The general problem Range and related statistics Deviation scores The variance and standard deviation Boxplots Review questions The General Problem Central tendency only deals with the center Dispersion Variability of the data around something The spread of the points Example: Mice and Music Mice and Music Study by David Merrell Raised some mice in quiet environment Raised some mice listening to Mozart Raised other mice listening to Anthrax Dependent variable is the time to run a straight alley maze after 4 weeks. Results Anthrax mice took much longer to run Much greater variability in Anthrax group See following graphs for Anthrax and Mozart We often see greater variability with larger mean The range Range and Related Statistics Distance from lowest to highest score Too heavily influenced by extremes The interquartile range (IQR) Delete lowest and highest 25% of scores IQR is range of what remains May be too little influenced by extremes Trimmed Samples Delete a fixed (usually small) percentage of extreme scores Trimmed statistics are statistics computed on trimmed samples. Definition Deviation Scores distance between a score and a measure of central tendency usually deviation around the mean Importance Variance Definitional formula Example See next slide Computing the Variance Computing the Variance Standard Deviation Definitional formula The square root of the variance Computational formula based on algebraic manipulation Makes it easier to calculate Computational Formula T ry o n e T ry o n e T ry o n e T ry o n e T ry o n e Estimators M ean Unbiased estimate of population mean () Define unbiased Long range average of statistic is equal to the parameter being estimated. Variance Unbiased estimate of 2 Estimators--cont. Using gives biased estimate Standard deviation use square root of unbiased estimate. Merrell’s Music Study SPSS Printout Treatment Mean Quiet 307.2319 Mozart 114.5833 Anthrax 1825.8889 Total 755.4601 The general problem N 23 24 24 71 WEEK4 Std. Deviation 71.8267 36.1017 103.1392 777.9646 Boxplots A display that shows dispersion for center and tails of distribution Calculational steps (simple solution) Find median Find top and bottom 25% points (quartiles) eliminate top and bottom 2.5% (fences) Draw boxes to quartiles and whiskers to fences, with remaining points as outliers Boxplots for comparing groups Combined Merrell Data Merrell Data by Group Review Questions What do we look for in a measure of dispersion? What role do outliers play? Why do we say that the variance is a measure of average variability around the mean? Why do we take the square root of the variance to get the standard deviation? Review Questions--cont. How does a boxplot reveal dispersion? What do David Merrell’s data tell us about the effect of music on m i c e?