# Likert Scales are the meaning of life: Dane

Likert Scales are the meaning of life: Dane Bertram Overview Basics Analysis Methods Worked Example Strengths Weaknesses dane.bertram CPSC 681 Likert Scales 1/16/20 Basics dane.bertram { Basics } CPSC 681 Likert Scales 1/16/20 Likert Scale \lick-urt\, n. { Basics } Who? Dr. Rensis Likert What? Psychometric response scale When? 1932 Where? Questionnaires Why? Obtain preference or degree of agreement dane.bertram CPSC 681 Likert Scales 1/16/20 Sample Likert Scale Question

{ Basics } Please indicate how much you agree or disagree with each of the following statements: Strongly disagree Somewhat disagree Neither agree nor disagree Somewhat agree Strongly agree 1. The U of C This is now website is easy to use 1 2 3 4 5 2. The My U of C website is easy to use. 1 2 3 4 5 3. The Peoplesoft Student Center website is easy to use. 1 2 3 4 5 dane.bertram CPSC 681 Likert Scales 1/16/20

Analysis Methods dane.bertram CPSC 681 Likert Scales { Analysis Methods } 1/16/20 Analysis Methods { Analysis Methods } Individual questions (ordinal data) Descriptive statistics Median Mode Range Inter-quartile range Not mean or standard deviation Non-parametric tests Mann-Whitney U test Wilcoxon signed-rank test Kruskal-Wallis test dane.bertram CPSC 681 Likert Scales 1/16/20 Analysis Methods Contd { Analysis Methods } Summed responses (interval data) Restrictions All questions use same Likert scale Defendable approximation to an interval scale Parametric tests Analysis of variance (ANOVA) Reduced to nominal levels of agree vs. disagree: Chi-square test Cochran Q test McNemar test dane.bertram CPSC 681 Likert Scales 1/16/20

Worked Example dane.bertram CPSC 681 Likert Scales { Example } 1/16/20 Worked Example { Example } Raw data Descriptive statistics Mann-Whitney U test Please indicate how much you agree or disagree with each of the following statements: Strongly disagree Somewhat disagree Neither agree nor disagree Somewhat agree Strongly agree 1. The U of C This is now website is easy to use 1 2 3 4 5 2. The My U of C website is easy to use. 1 2 3 4 5 3. The Peoplesoft Student Center website is easy to use.

1 2 3 4 5 dane.bertram CPSC 681 Likert Scales 1/16/20 Raw Data Participant ID { Example } Q1. U of C Q2. My U of C Q3. Peoplesoft 1 4 4 3 2 3 4 3 3 4 3 2 2 3 4 5 3

3 6 4 2 2 7 3 3 3 8 4 4 4 9 3 4 3 10 2 5 2 11 2 4 2 4 1 3 1 3

2 14 2 2 3 15 4 3 3 16 1 1 2 4 5 12 13 Category MSc PhD Table 1. Raw Data dane.bertram CPSC 681 Likert Scales 1/16/20 Descriptive Statistics { Example } Median Mode Range Inter-quartile Range Q1. U of C 3

4 4 2 Q2. My U of C 3 3 4 1.25 Q3. Peoplesoft 3 3 2 1 Range Inter-quartile Range Table 2. Descriptive Statistics 1A Median Mode MSc PhD MSc PhD MSc PhD MSc PhD Q1. U of C 4 2 4

2 3 3 1 1.5 Q2. My U of C 3 3 3 4 2 4 1 2.25 Q3. Peoplesoft 3 2.5 3 3 2 1 0.5 1 Table 3. Descriptive Statistics 1B dane.bertram CPSC 681 Likert Scales 1/16/20 Descriptive Statistics Contd Q1. U of C Q2. My U of C Q3. Peoplesoft

{ Example } Strongly disagree Somewhat disagree Neither agree nor disagree Somewhat agree Strongly agree # 2 4 3 6 1 % 13% 25% 19% 38% 6% # 2 2 6 5 1 % 13% 13% 38% 31% 6%

# 0 6 8 2 0 % 0% 38% 50% 13% 0% Somewhat agree Strongly agree Table 4. Descriptive Statistics 2A Strongly disagree Q1. U of C Q2. My U of C Q3. Peoplesoft Somewhat disagree Neither agree nor disagree MSc PhD MSc PhD MSc PhD MSc PhD MSc

PhD # 0 2 1 3 2 1 4 2 1 0 % 0% 25% 13% 38% 25% 13% 50% 25% 13% 0% # 0 2 1 1 4 2

3 2 0 1 % 0% 25% 13% 13% 50% 25% 38% 25% 0% 13% # 0 0 1 4 4 4 2 0 0 0 % 0% 0% 25%

50% 50% 50% 25% 0% 0% 0% Table 5. Descriptive Statistics 2B dane.bertram CPSC 681 Likert Scales 1/16/20 Mann-Whitney U test { Example } Requirements: Non-parametric test Two samples must be statistically independent Observations must be on an ordinal scale Null hypothesis: Equal probability that an observation from one sample will exceed an observation from the other sample dane.bertram CPSC 681 Likert Scales 1/16/20 Step 1: Calculate U statistic { Example } Combine observations from both samples Write down observations in rank-order Label which sample each observation came from Alternate between samples when repeated values appear in both Tie Tie Tie Tie Rankordered:

1 1 2 2 2 2 3 3 3 4 4 4 4 4 4 5 Origin sample: P P M P P P M P M M P M P

M M M dane.bertram CPSC 681 Likert Scales 1/16/20 Step 1: Calculate U statistic { Example } For each observation from sample 1 (MSc students): Move left-to-right Count 1 for each observation from sample 2 (PhD students) occurring after it in the list When there is a tie, count 0.5 Add all these counts together to form UMSc Tie Rank1 ordered: Count for first Origin sample: P dane.bertram 1 2 2 2 2 3 3 3 4 4 4 4 4

4 5 P M P P P M P M M P M P M M M ++ 11 ++ 11 0.5 0.5 } Count Count:= 1 2 2 MSc response: ++ 11 CPSC 681 Likert Scales ++ 11 ++ 11

= =5.5 5.5 1/16/20 Step 1: Calculate U statistic Count for second MSc response: { Example } Tie Rankordered: 1 1 2 2 2 2 3 3 3 4 4 4 4 4 4 5 Origin sample: P P M P P

P M P M M P M P M M M +1 +1 0.5 0.5 + 1 ++ 11 } Count Count:= ++ 11 = =2.5 5.5 Count for third MSc response: Rankordered: 1 1 2 2 2 2 3

3 3 4 4 4 4 4 4 5 Origin sample: P P M P P P M P M M P M P M M M +1 +1 Count Count:=

dane.bertram 0.5 +1 CPSC 681 Likert Scales +11 ++ 11 = =2 5.5 1/16/20 Step 1: Calculate U statistic { Example } Sum these counts together: UMSc = 5.5 + 2.5 + 2 + 1.5 + 0.5 + 0 + 0 + 0 = 12 Similarly, calculate UPhD: UPhd = 8 + 8 + 7.5 + 7 + 7 + 6.5 + 4.5 + 3.5 = 52 Sanity check: U1 + U2 = (# of observations in S1) x (# of observations in S2) dane.bertram CPSC 681 Likert Scales 1/16/20 Step 2: Critical values table { Example } Use the lower of the two U stats (UMSc = 12) with: n1 = # of observations in S1 n2 = # of observations in S2 = level of significance If below table value: Reject null hypothesis Samples are significantly different at the level Table 6. Mann-Whitney U Distribution Critical Values dane.bertram CPSC 681 Likert Scales

1/16/20 Why does it not suck? { Strengths } Simple to construct Generally a highly reliable scale Easy to read and complete for participants Fun for the whole family! dane.bertram CPSC 681 Likert Scales 1/16/20 Ok then, what does suck? { Weaknesses } Central tendency bias Fence riding Acquiescense bias Try to please you Social desirability bias Portray themselves favourably Lack of reproducibility Difficult to demonstrate validity Did you measure what you set out to measure? dane.bertram CPSC 681 Likert Scales 1/16/20 Questions? Thank you! Danes presentation totally rocked my socks:

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