Statistics I JLCP 782
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Date Created: 09/28/15
JLCP 782 Statistics I Homework review I Reading statistical equations some basics I Understanding distributions I Reading raw data into SPSS Reading Statistical Equations Sample size A vectorof data A summation sign Sum all X39s A more complete version Xi EXI39 Grouped versus Ungrouped Distributions I Difference between grouped and ungrouped I Group distribution rules I mutually exclusive I exhaustive I equal interval width I first class contains lowest last class contains highest I Steps I Determine number of class intervals I Determine width of interval W Wm em I Make the intervals Bar charts I For nominal or ordinal level data I Bar chart bars not connected I All possible values are included I Bar charts can be vertical or horizontal I Advantages of bar charts over pie charts Bar Chart in SPSS graph barfsimple DV by IV Histograms I Like a bar chart but for interval or better data I Might be grouped or ungrouped I Ungrouped shows frequency for each value I Grouped shows frequency for a class interval I Might need to play with class interval to find optimal graphical display Line Graph I Simple line graph is similar to a histogram I Data should be interval or higher ordinal might be okay I Handles a large number of values well I Illustrate in SPSS Distribution Shape I Normal I Skewed positive and negative I Kurtosis leptokurtic and platykurtic I See histogram with normal distribution overlay Measures of Central Tendency I Mean median and mode I Most common value I There might be multiple modes bimodal I Useful for nominal and ordinal data I Advantages simple easy to calculate very general I Disadvantages ignores information might be misleading Median I Middle value if odd number of numbers I Mean of the two middle most numbers if even number of numbers I Not affected by extreme values I Useful for skewed interval ratio data eg income I Also appropriate for ordinal data I Median observation is found by N 1 T Median I Median is the 50th percentile I What is a percentile I How is it different than a percent I Can someone be at the 100th percentile Median I Adva nta ges I only one me dian I intuitive appeal I not influenced by extreme values skewl outliers numbers I The sum of all the numbers divided by the number39of Y in n l Balance point in the distribution I As such the mean is pulled by extreme values Computation of the mean gtlt H N4gtHOOQJONJgtMUW Y 5611 509 Characteristics of the Mean I Least squares property I Balance point I Deviations equal 0 Advantages and Disadvantages of the Mean I intuitively appealing I uses all of the data I statistically efficient I distorted by outliers or skewed data How to they Compare How do the mean median and mode relate to one another I In a unimoda symmetric distribution they are the same I Positively skewed distribution mode lt median lt mean I Negativer skewed distribution mean lt median lt mode Which to use I Mode you are interested in the most common Have nominal or ordinal data I Mean you are interested in the average and the distribution is not seriously skewed Have interval or higher data I Median you are interested in the average and the distribution is seriously skewed Have interval or higher data I Median you are interested in the midpoint Measures of Dispersion Variability I Variance ratio I Range Minimum and Maximum I Interquartile Range I Variance and the Standard Deviation Variance ratio VR I For nominal or ordinal data I The larger the VR the more dispersion I Equals the proportion of cases not in the modal category VR 17 fmodal n I VR is at maximum when all categories have the same frequency I If there are 4 categories and 25 of the cases in each then VR is 75 values in the data I Simply the difference between the maximum and minimum Interquartile Range I Difference between the 25th and 75th percentiles I Identifies the middle 50 of the cases I SPSS can find these values for you I Doing it by hand is not always easy I If n equals 157 157 data points then I 25th percentile is the 395th case n171571 25th rank 4 3915 I And the 75th percentile is 1185 75th rank 315 11815 I Find the average between the 39th and 40th ranked values and the 118th and 119th ranked values and you have your IQR Variance and Standard Deviation I Building block for a lot of data analysis I Used to standardize measures I Based on the squared distances between the individual and the mean I Illustrate averaging deviations around the mean I Population versus sample values Definitional formulas Definitional formula sample 52Xi72 n71 sVs2 Computational formula XiZ 7 52 Z n n71 Advantages of Computations formula l Easier to compute really I No rounding problems more accurate when done by hand Interpreting the Standard Deviation I Roughly 15th of the range I In a normal distribution 68 of the cases fall within 1 standard deviation of the mean above and below I In a normal distribution 95 plus a little fall within 2 standard deviations of the mean above and below SPSS Syntax desc var VARNAME statistics mean stddev variance range min max examine var VARNAME plot none percentiles5102550759095 statistics descriptives