Introductory Biostatistics: Week 2 Solutions for Unit 2 - Summarizing Data, Study notes of Biostatistics

Download Introductory Biostatistics: Week 2 Solutions for Unit 2 - Summarizing Data and more Study notes Biostatistics in PDF only on Docsity! PubHlth 540 Introductory Biostatistics Page 1 of 10 Unit 2 - Summarizing Data Week #2 - Practice Problems Solutions 1. A stem and leaf diagram might come in handy. Stems are shaded, leaves are not. 3 68851865 3 1 5 5 6 6 8 8 8 4 50165165310 → 4 0 0 1 1 1 3 5 5 5 5 39113 5 1 1 3 3 9 6 90 6 0 9 ( ) MEAN x n X = n x i i so = = = = 1 1 1156 4446 445 1 26 Σ . . ( ) MEDIAN n x x First solve Median is midpoint of 13 and 14 observation. so th th +⎛ ⎝⎜ ⎞ ⎠⎟ = +⎛ ⎝⎜ ⎞ ⎠⎟ = = + = 1 2 26 1 2 135 1 2 41 43 42 . ~ ~ MODE RANGE This sample is tri - modal Maximum - Minimum so range 38 4145 69 31 38 , , = − = … wk2_solutions.doc PubHlth 540 Introductory Biostatistics Page 2 of 10 VARIANCE Let’s save ourselves the trouble of a very long brute force formula by using the formula for grouped data. Let j index the unique values. There are 14 unique values. j Xj fj ( )x xj − 2 ( )f x xj j − 2 1 31 1 182.25 182.25 2 35 2 90.25 180.50 3 36 2 72.25 144.50 4 38 3 42.25 126.75 5 40 2 20.25 40.50 6 41 3 12.25 36.75 7 43 1 2.25 2.25 8 45 3 0.25 0.75 9 46 2 2.25 4.50 10 51 2 42.25 84.50 11 53 2 72.25 144.50 12 59 1 210.25 210.25 13 60 1 240.25 240.25 14 69 1 600.25 600.25 TOTALS 26 1998.50 ( ) S f x x f So Sj j j j j 2 1 14 2 1 14 2 1 1998 50 25 79 94= − ⎛ ⎝⎜ ⎞ ⎠⎟ − = == = Σ Σ . . Standard deviation S S So S= =2 894. … wk2_solutions.doc PubHlth 540 Introductory Biostatistics Page 5 of 10 1C. REMINDER - Use the same scale when comparing two groups. Group Patients Controls Mean 44.5 27.0 Median 42 26 P25 38 25 P75 51 28 Interquartile Range (IQR) 13 3 P25-(1.5)(IQR) 18.5 20.5 P75+(1.5)(IQR) 70.5 32.5* Min 31* 25* Max 69* 34 *=Whisker Notes on Whiskers 1) IF P25 - (1.5) (IQR) < minimum of the actual data, so use minimum of actual data instead 2) IF P75 + (1.5) (IQR) > maximum of the actual data, so use maximum of actual data instead Patients with panic disorder have ZAS scores that are higher than those of controls. As well, ZAS scores of patients with panic disorder have more variability. HEALTHY PANIC 25 30 35 40 45 50 55 60 65 70 Exercise #2C - Box and Whisker PlotExercise #1C – Box and Whisker Plot ZA S Sc or e Healthy (n=21), Panic Disorder (n=26) … wk2_solutions.doc PubHlth 540 Introductory Biostatistics Page 6 of 10 2A. Class Class Relative Cumulative Cumulative Endpoints Midpoint Frequency Frequency Frequency Relative Freq. 5-14.99 10 5 .067 5 .067 15-24.99 20 10 .133 15 .200 25-34.99 30 20 .267 35 .467 35-44.99 40 22 .293 57 .760 45-54.99 50 13 .173 70 .933 55-64.99 60 5 .067 75 1.000 TOTALS 1.000 2B. A cumulative relative frequency polygon for grouped data is, unfortunately, not straightforward in SAS or Stata or SPSS or minitab. Solution using Excel. Step 1: Enter your “x” and “y” points into your worksheet such that “x” = Endpoint of class interval “y” = Cumulative relative frequency for the interval note – Be sure to include an (x,y) = (0,0) x=age y=cumulative relative frequency 0 0 15 0.067 25 0.2 35 0.467 45 0.76 55 0.933 65 1 … wk2_solutions.doc PubHlth 540 Introductory Biostatistics Page 7 of 10 Step 2: Use the chart wizard in excel as follows. Highlight the data you want to plot Click on the chart wizard from the upper toolbar Under Chart Type: - Select XY (Scatter) Under Chart sub-type - Highlight the plot with the dots connected Click Next You should see the following Click Next … wk2_solutions.doc