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Chapter 9 Describing Variations in Data Copyright Kaplan University 2009 A variable is… A single characteristic that can vary and can be measured Medical Variables: Biological Differences Presence, Absence & Stage of Disease Conditions of Measurement Techniques of Measurement Measurement Error How to Interpret Data The Decision Factor Decide if data is “quantitative” or “qualitative” Identify any variable which may affect data usage Types of Variables Nominal: “the name game”, classifying in a nonnumerical way. Ex: Male/Female; Yes/No; A,B,AB,O (BLOOD TYPES) Each classification can be given a numerical data code or point for ease of statistical inference. Example: Male = 1; Female = 2. Gender Frequency 1 Percent .8 Valid Percent .8 Cumulative Percent .8 1.00 44 36.4 36.4 37.2 2.00 74 61.2 61.2 98.3 3.00 2 1.7 1.7 100.0 121 100.0 100.0 Valid Total 1.00 = Male 2.00 = Female 3.00 = Unknown Types continued… Dichotomous or Binary Variable: Variables that reflect two extreme opposites Example: Living/Dead Dichotomous and nominal variables are also called “discrete variables” because the categories are different from one another Variables, continued Ordinal Variables: Ranked variables that follow an order. Example: Surveys that ask participants to rank answers/opinions as “very satisfied”; “satisfied” and “not satisfied” Continuous (Dimensional) Variables: Measurements which may reflect a continuous line of data. Example: Height, Weight, Blood Pressure, other readings that can change regularly Ratio Variables: - A continuous scale in which “0” has a meaning Fahrenheit/Celsius Scale Both pictures are taken from google images.com Centrigrade Scale Methods of Documenting Observations Frequency Table Consists of a x and y axis and is used to show two characteristics that relate to one another X Axis = Scores Y Axis = Frequency of each score Score Below 75 Frequency 4 76 - 80 14 81 - 85 2 86 - 90 8 91 - 95 5 96 - 100 1 Taken from google images Combining Data The grouping of similar values together in order to simplify examination of the data Of the two sets of birth weights of babies at Cabbage Patch Hospital which is easier to decipher? 1-3 pounds = 10 4-6 pounds = 45 7-9 pounds = 25 10-12 pounds = 12 13+ pounds = 8 2,11,13,14,16,12,10,7,6,8,2, 6,1,12,11,10,9,4,7,2,9,1,8 7,2,6,1,8,7,6,5,6,3,5,2,4,1 2,13 Frequency Distribution Recording observations of one variable by using X Axis for variable and Y Axis for the frequency of occurrence Look at Table 9-2 and 9-3 (pp. 142, 143) Which has more interpretive meaning to you? Why? Gaussian Distribution Also Known as “normal distribution” Real data seldom follows this slope The larger the data, the more Gaussian or “bell shaped” it would look Images taken from google images.com Types of Visual Representation Histogram of Smokers Age at Last Birthday 60 40 20 0 Smoke >=2 PackDay Now smoke>=1 and <2 PackDay Now Smoke<1PackDay Now >=1 PackDay and Quit <3 Years >1 PackDay and Quit >=3 Year <=1 PackDay and Quit <=3 Year <=1 PackDayand Quit >=3 years Never Smoked Smoking Habits Histogram: A bar graph of vertical bars. The area of the bars represent proportions of all observations that fall within range of the bar Frequency Polygon: This is a histogram minus the bars which are replaced by dots which are then connected Images taken from google images.com Measurements Mode: Most commonly seen value in a group of measurements Example: 6 9 6 8 10 6 4 4 8 11 6 10 The mode is 6 Median: Middle observation of a data group is derived by putting numbers in order and finding the center number. If there are an even amount of data points, take the middle two and take an average. Median continued… Example: 1 4 9 20 23 27 31 48 56 58 23 + 27/2 = 25 Mean: The average of a group of data points (add all numbers then divide by the number of numbers) Example: Using the numbers above the mean is 27.7 Your Turn (time limit: 5 minutes) Compute the Mode, Median and Mean of the following monthly glucose readings for Fred: Jan = 120 July = 98 Feb = 100 Aug = 127 Mar = 110 Sept = 134 April = 128 Oct = 141 May = 138 Nov = 128 June = 121 Dec = 146 Answer Mode = 128 Median = 127.5 Mean = 124.5 Questions… Homework Time This chapter covered a great deal, so… Please re-read the remainder of the chapter beginning with page 149 – “Problems in analyzing a Frequency Distribution. This information is a review/continuance of what we have covered tonight Please drop me an e-mail after you have re-read this area and indicate if you have any further questions or if you are in complete understanding of the information. Any Further Questions