The calculation of percentages and means from data in a Blackboard Enterprise Survey
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1 The calculation of percentages and means from data in a Blackboard Enterprise Survey This paper provides an overview of the results displayed in reports generated from a Blackboard Enterprise Survey. For many staff, the displayed percentage value does not match the value they obtain when manually calculating the result. The results are predictably different. This sheet eplains why and how to convert this figure to an arithmetic mean value. In the eample, we are going to look at a typical 5 point Likert question which has the following possible responses: Answers Strongly agree (Points: 5) Agree (Points: 4) Neither agree nor disagree (Points: 3) Disagree (Points: 2) Strongly disagree (Points: ) The output from 7 respondents may look something like this stacked bar graph from a Blackboard Enterprise Survey: This may look more familiar if plotted as a table and standard bar chart, which makes it clearer that one response (Strongly disagree) has not been selected by any respondent: count Strongly agree 2 Agree Neither agree or disagree Disagree 3 Strongly disagree 0 We can add an etra column to this table representing the points previously assigned to each response: count points Strongly agree 2 5 Agree 4 Neither agree or disagree 3 Disagree 3 2 Strongly disagree 0
2 For most people the net logical step is to calculate the product of the count and the points (e.g. taking the first row, 2 5 = 0): count points product Strongly agree Agree 4 4 Neither agree or disagree 3 3 Disagree Sum Total 23 We are now in a position to calculate the arithmetic mean value: Mean Value = Number of Respondents = 23 7 = To convert this to a percentage we need to calculate the maimum possible number of points (i.e. the total of the product values if everyone chose the option Strongly agree): Maimum Possible Points = Total number of responses Maimum score = 7 5 = 35 We can then plug this value into the equation: Percentage = Maimum Possible Points = = 65. 7% The point to note here is that this is not the same as the figure displayed in Blackboard s Enterprise Survey Report (57%). Why not?
3 There are a few problems with these measures. In the case of this eample, the mean always lies in the range to 5, with a value of 3 (not 2.5) indicating an even spread of values. Moreover, the value of this statistic is related to the number of responses (so you shouldn t directly compare a mean from a 4-point Likert question (which will have a value in the range to 4 and a value of 2.5 indicating an even spread) with a mean from a 5 point Likert question (which will have a value in the range to 5 and a value of 3 indicating an even spread). For a 5 point Likert the percentage figure will be in the range 20% to % with a value of 60% (not 50%) indicating an even spread. For a 4 point Likert the percentage figure will be in the range 25% to % with a value of 62.5% indicating an even spread. In both cases the percentage results will never be zero unless no-one has responded. This makes comparison difficult and sometimes counter-intuitive (particularly when results are epressed as percentages when 50% is normally taken to indicate a midpoint). To try and address this issue, Blackboard rescale all results so that they lie in the range 0% to % (regardless of the number of Likert points) where 0% indicates everyone selected the response with the lowest point value (in our eample Strongly disagree), 50% represents an even spread and % that every respondent selected the response with the highest point value (in our eample Strongly agree). This eample shows how Blackboard calculate the percentage displayed on the Enterprise Survey report. We begin as before with counts and points: count points Strongly agree 2 5 Agree 4 Neither agree or disagree 3 Disagree 3 2 Strongly disagree 0 Blackboard then assign percentage values for each response so that the highest point question gets %, the lowest 0% and the others get values based on this formula Step value = (number of categories ) = (5 ) = 4 = 25%
4 So we assign the percent values: %, 75%, 50%, 25% and 0% count points percent Strongly agree 2 5 Agree 4 75 Neither agree or disagree 3 50 Disagree We can then dispense with the points column and calculate a new product column, this time the product of the count and percentage values (so in the first row 2 % = 200%): count percent product Strongly agree Agree Neither agree or disagree Disagree Sum Total 400 As before to calculate a percentage we need to calculate the maimum possible product (i.e. the total of the product values if everyone chose the option Strongly agree): Maimum Possible Points = Total number of responses Maimum percent = 7 % = 700% We can then plug this value into the equation: Percentage = Maimum Possible Points = = 57. 4% This matches the value displayed in a Blackboard Enterprise Survey:
5 Converting Values for Reports If you want to convert values from the Blackboard percentage displayed on an Enterprise Survey Report you can use these formulae: 5 Point Likert Questions Normal Percentage = (0.8 Blackboard Percentage) + 20 Arithmetic Mean = (0.04 Blackboard Percentage) + If you have the Blackboard percentage value in an Ecel spreadsheet in the cell A2 Normal Percentage = (0.8 A2) + 20 Arithmetic Mean = (0.04 A2) + 4 Point Likert Questions Normal Percentage = (0.75 Blackboard Percentage) + 25 Arithmetic Mean = (0.03 Blackboard Percentage) + If you have the Blackboard percentage value in an Ecel spreadsheet in the cell A2 Normal Percentage = (0.75 A2) + 25 Arithmetic Mean = (0.03 A2) + Dr Malcolm Murray
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