# Working in Excel

## Part 11.1 Summarizing the data

We will be using data collected from an internet survey sponsored by the German government.

First, download the survey data and documentation:

• Download the data. Read the Data dictionary tab and make sure you know what each variable represents. (Later we will discuss exactly how some of these variables were coded.)
• The paper ‘European values study longitudinal data file 1981–2008’ gives a brief summary of how the survey was conducted. You may find it helpful to read it before starting on the questions below.
1. While contingent valuation methods can be useful, they also have shortcomings. Read Section 5 of the paper ‘Introduction to economic valuation methods’ (pages 16–19), and explain which limitations you think apply particularly to the survey we are looking at.
Likert scale
A numerical scale (usually ranging from 1–5 or 1–7) used to measure attitudes or opinions, with each number representing the individual’s level of agreement or disagreement with a particular statement.

Before comparing between question types, we will first compare the people assigned to each question type to see if they are similar in demographic characteristics and attitudes towards related topics (such as beliefs about climate change and the need for government intervention). Attitudes were assessed using a 1–5 Likert scale, where 1 = strongly disagree, and 5 = strongly agree.

1. Re-code or create the variables as specified:
• Reverse-code the following variables (so that 1 is now 5, 2 is now 4, and so on): cog_2, cog_5, scepticism_6, scepticism_7. (Hint: One way to do this is to create a new variable and use Excel’s IF function to fill in the values of the new variable based on the values of the original variable.)
• For the variables ‘WTP_plmin’ and ‘WTP_plmax’, create new variables with the values replaced as shown in Figure 11.1 below (these are the actual amounts, in euros, that individuals selected in the survey, and will be useful for calculating summary measures later).
Original value New value
1 48
2 72
3 84
4 108
5 156
6 192
7 252
8 324
9 432
10 540
11 720
12 960
13 1,200
14 1,440

WTP survey categories (original value) and euro amounts (new value).

Figure 11.1 WTP survey categories (original value) and euro amounts (new value).

1. Create the following indices, giving them an appropriate name in your spreadsheet (make sure to use the reverse-coded variable where relevant):
• Belief that climate change is a real phenomenon: Take the mean of scepticism_2, scepticism_6, and scepticism_7.
• Preferences for government intervention to solve problems in society: Take the mean of cog_1, cog_2, cog_3, cog_4, cog_5, and cog_6.
• Feeling of personal responsibility to act pro-environmentally: Take the mean of PN_1, PN_2, PN_3, PN_4, PN_6, and PN_7.
Cronbach’s alpha
A measure used to assess the extent to which a set of items is a reliable or consistent measure of a concept. This measure ranges from 0–1, with 0 meaning that all of the items are independent of one another, and 1 meaning that all of the items are perfectly correlated with each other.

When creating indices, we may be interested to see if each item used in the index measures the same underlying variable of interest (known as reliability or consistency). There are two common ways to assess reliability: either look at the correlation between items in the index, or use a summary measure called Cronbach’s alpha (this measure is used in the social sciences).

Cronbach’s alpha is a way to summarize the correlations between many variables, and ranges from 0 to 1, with 0 meaning that all of the items are independent of one another, and 1 meaning that all of the items are perfectly correlated with each other. While higher values of this measure indicate that the items are closely related and therefore measure the same concept, with values that are very close to 1 (or 1) we could be concerned that our index contains redundant items (for example, two items that tell us the same information, so we would only want to use one or the other, but not both). You can read more about this in the paper ‘Using and interpreting Cronbach’s Alpha’.

1. Calculate correlation coefficients and interpret Cronbach’s alpha:
• For one of the indices you created in Question 3, create a correlation table to show the correlation between each of the items in the index. Figure 11.2 shows an example for Question 3(a). (Remember that the correlation between A and B is the same as the correlation between B and A, so you only need to calculate the correlation for each pair of items once.) Are the items in that index strongly correlated?
• The Cronbach’s alpha for these indices are 0.66, 0.71, and 0.85 respectively. Interpret these values in terms of index reliability.
scepticism_2 scepticism_6 scepticism_7
scepticism_2 1
scepticism_6   1
scepticism_7     1

Correlation table for items in Question 3(a).

Figure 11.2 Correlation table for items in Question 3(a).

Now we will compare characteristics of people in the dichotomous choice (DC) group and two-way payment ladder (TWPL) group (the variable ‘abst_format’ indicates which group an individual belongs to). Since the groups are of different sizes, we will use percentages instead of frequencies.

1. For each group, create separate tables to summarize the distribution of the following variables:

• gender (‘sex’)
• age (‘age’)
• number of children (‘kids_nr’)
• household net income per month in euros (‘hhnetinc’)
• membership in environmental organization (‘member’)
• highest educational attainment (‘education’).

Without doing formal statistical tests, do the two groups of individuals (DC and TWPL) look similar in demographic characteristics?

1. Create summary tables as shown in Figure 11.3 for each index you created in Question 3. Without doing formal statistical tests, do the two groups of individuals look similar in the attitudes specified?
Mean Standard deviation Min Max
DC format
TWPL format

Summary table for indices.

Figure 11.3 Summary table for indices.

## Part 11.2 Comparing willingness to pay across methods and individual characteristics

Before comparing WTP across question formats, we will summarize the distribution of WTP within each question format.

1. For individuals who answered the TWPL question:
• Use the variables ‘WTP_plmin’ and ‘WTP_plmax’ to create column charts (one for each variable) with frequency on the vertical axis and category (the numbers 1–14) on the horizontal axis. Describe characteristics of the distributions shown on the charts.
• Using the variables you created in Question 2(c) in Part 11.1, make a new variable that contains the average of the two variables (the average of the minimum and maximum willingness to pay).
• Using the variables you created in Questions 2(c) in Part 11.1 and 1(b) here, calculate the mean and median willingness to pay.
• Using the variable from Question 1(b), calculate the correlation between the average WTP and the demographic and attitudinal variables. Interpret the relationships implied by the coefficients.
1. For individuals who answered the DC question:
• Each individual was given one amount and had to decide ‘yes’, ‘no’, or ‘no vote/abstain from deciding’. Make a PivotTable showing the frequency of ‘DC_ref_outcome’, with ‘costs’ as the row variable and ‘DC_ref_outcome’ as the column variable.
• Use this table to calculate the percentage of individuals who voted ‘no’ and ‘yes’ for each amount (in other words as a percentage of the row total, not the overall total). Count individuals who chose ‘abstain’ as voting ‘no’.
• Make a scatterplot showing the ‘demand curve’, with percentage of individuals who voted ‘yes’ as the vertical axis variable and amount (in euros) as the horizontal axis variable. (To connect the points, use the chart option ‘Scatter with Straight Lines and Markers’.) Describe features of this ‘demand curve’ that you find interesting.
• Repeat Question 2(b), this time excluding individuals who chose ‘abstain’ from the calculations. Plot this new ‘demand curve’ on the chart created for Question 2(c). Do your results change qualitatively, depending on how you count individuals who did not vote?
1. Compare the mean and median WTP under both question formats:
• Complete Figure 11.4 and use it to calculate the difference in means (DC minus TWPL), the standard deviation of these differences, and the number of observations. (The mean of DC is the mean of ‘DC_ref_outcome’ for individuals who voted ‘yes’.)
• Use Excel’s CONFIDENCE.T function and the calculated values for Question 3(a) to determine the confidence interval ‘width’ (distance between the mean and one end of the interval) of the difference in means using a 5% significance level. Discuss the statistical significance of your findings.
• Does the median WTP look different across question formats? (You do not need to do any formal statistical testing.)
• Using your answers to Questions 3(a)–(c), would you recommend that governments use the mean or median WTP in policy-making decisions? (That is, which measure is more robust to changes in the question format?)
Format Mean Standard deviation Number of observations
DC
TWPL

Summary table for WTP.

Figure 11.4 Summary table for WTP.