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Performing A Two-tailed Equal Variance T-Test in Excel

Dive into the world of stated preference techniques and dive into the intricacies of assessing individuals' willingness to pay for environmental goods and services. This problem set delves into the concept of protest responses, data analysis, and statistical tests in Excel to shed light on how different income groups perceive and value specific environmental projects. Learn about the challenges and insights that arise when assessing preferences and understanding the economics of environmental choices.

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Problem Description:

This Data Analysis Homework explores the concept of "stated preference techniques" used in valuation methods to estimate changes in utility associated with anticipated improvements in ecosystem services. It aims to evaluate people's willingness to pay by directly questioning the value they assign to environmental goods or services. The homework delves into the challenges of "protest responses" and their impact on willingness to pay estimations. It also involves data analysis and statistical tests to understand how different income groups perceive and are willing to pay for a specific environmental project.

Solution

  1. Explain the meaning of “stated preference techniques”, including its goal and when it is appropriate to use.

    2. “Stated preference techniques” are a set of valuation methods in which individual’s responses about their preferences are used to estimate change in utility associated with an anticipated increase in quality or quantity of an ecosystem service(s). Its goal is to evaluate people’s willingness to pay by asking them direct questions regarding the value they give to certain environmental goods or services. Stated preference techniques are useful in eliciting monetary values or total economic value and in ex-ante analysis. It is also appropriate to use when important variables such as environmental quality and regulations, etc. do not change or are absent, or there is a poor quality of data regarding behavioral variables. These techniques help determine consumer’s behavioral pattern towards a certain product, or their willingness to pay for its valued features.

  2. What does a “protest response” mean and why is it an issue?

    3. “Protest response” is considered as an issue of not stating the true ‘willingness to pay’ (WTP) value for the good for some reason. It is considered to be an issue, because it creates a problem of selection bias, indicating that a group of people who refused to pay or have ‘zero willingness to pay’ makes it difficult to estimate true ‘willingness to pay’ (WTP) while having others with positive responses.

  3. Use the Data – No Protest sheet in the Excel document posted in iLearn to copy over data and eliminate protest responses, where the variable PROTEST = e, f, or g, by deleting the whole row for that observation. You can also see the Living Roof survey posted as a reference and see questions in context. We shall leave in place any “warm glow” responses for the yes’s, following Loomis et al. old growth study.

    4. There were three observations where PROTEST = g; the entire row or response was removed for the basis of further analysis.

  4. On the Excel Data analysis sheet, fill in Table 1. with the percent responses to the first bid level asked in each survey version (WTP1V1-15, WTP1V2-25, WTP1V3-40 in datasheet).

    5. The percent responses of “yes” to the first bid level asked in each survey version i.e., WTP1V1-15, WTP1V2-25, WTP1V3-40 is 21.21%, 15.15%, and 15.15% respectively.

  5. Generate a “column” chart and plot the three data points in your Excel document. Write here in the space below the pattern of responses as the initial bids get higher. Explain in two complete sentences minimum.

    6. As the initial bids get higher, the percent responses reduce at first and then get constant. This indicates that more people are interested in 15-item surveys compared to 25-item and 40-item surveys, and the rate of response gets consistent as the number of items/ questions in the survey is increasing from 25 to 40.

  6. On the Data analysis sheet in Table 2, engage the formulas by adding the = sign to the formula in each of the cells to get upper and lower bound Turnbull willingness-to-pay estimators like our example in class, plus the Kaplan-Meier-Turnbull (KMT) lower bound (only) estimator using the formula from class slides (and already embedded in your Excel sheet). State here in a sentence how you would report your results for a mean WTP measure using these measures.

    7. Using both the Turnbull estimator and the KMT version, the lower-bound mean WTP is calculated to be 6.97, indicating that consumers are willing to pay $6.97 minimum for the product at the initial bid. Using the Turnbull estimator, the upper-bound mean WTP is calculated to be $20.90, indicating that consumers are willing to pay $20.90 maximum for the product at the initial bid.

  7. In Table 3 of the Data analysis sheet, reports the percentage patterns for each version according to the yes-yes, yes-no, no-yes, and no-no patterns to the “double-bounded” method of asking the WTP question. Report for each version in the Table.
  8. Look at Carson et al’s Exxon Valdez paper on page 271 and read the paragraph explaining their results across survey versions in Table IV of the paper. Using their exposition as a guide, describe in a similar manner the pattern of responses you observe in the living roof survey using the follow-up sequence of WTP questions in your Table 3.

    9. The percentage patterns for each version highlighted that the yes-yes responses would be expected to fall as the dollar amount the respondent is asked to pay increases from $5 in version 1 (i.e., 15 percent say yes to $5) to $25 in version 3 (i.e., 9 percent to $25). Furthermore, the no-no responses would be expected to slightly increase as the dollar amount the respondent is asked to pay increases from $25 in version 1 (i.e., 73 percent say no to $25) to $50 in version 3 (i.e., 76 percent to $50). The no-no responses to version 1 define the upper bound on the percentage of respondents who may not care about protecting wildlife and wetlands habitat. It should be noted, though, that this group of respondents is also likely to include those who do not think that the Joaquin Valley Drainage Program will work or who believe that the Jones and Stokes Associates company should pay the entire cost of the plan.

  9. On the Data analysis sheet, starting in col. N, group the 0/1 responses to the first WTP question across all versions by “low” income (INCOME = 1,2) versus “high” income (INCOME = 3,4). Follow the instructions in the blue box to report the percentage of yes responses and simple averages by income group on the Excel sheet.
  10. Conduct a t-test in the space provided for the two-tailed equal variance t-test using instructions in the sheet to see if these average WTPs by low- and high-income groups are statistically different. Sample instructions for t.test in Excel: https://support.microsoft.com/en-us/office/t-test-function-d4e08ec3-c545-485f-962e-276f7cbed055. Explain here in one sentence the result of the t-test, the p-value, and whether the p-value tells you if your test was significant at the 10% level or better.

    11. Using a two-tailed equal variances t-test, the average WTPs by low- and high-income groups are found to be not statistically different (p = 0.1414) at a 10% level. In other words, average WTPs in the low-income group are similar to average WTPs in the high-income group.

  11. Repeat the t-test with a one-tailed, equal variance test and report the results here as you did in above.

    12. Using one-tailed equal variances t.test, the average WTPs by low- and high-income groups are found to be statistically different (p = 0.00000089) at 0.1% level. This infers that the high-income group is willing to pay higher on average as compared to the low-income group.

  12. Repeat the t-test with a two-tailed, unequal variance test and report the results here as you did above.

    13. Using a two-tailed unequal variances t-test, the average WTPs by low- and high-income groups are found to be statistically different (p = 0.0058) at a 1% level. This infers that the high-income group is willing to pay higher on average as compared to the low-income group.

  13. Table V data of the Carson et al. paper is recorded on the “Exxon Valdez” sheet in your Excel file. In col. I follow instructions to reproduce results from the third paragraph on p. 272 of the paper (i.e. multiply the density in each interval by the lower bound (LB) of the interval and sum) to get the mean LB WTP.
  14. In col. K and L, follow blue-box instructions to get the KMT estimate of WTP.
  15. In col. P and Q, follow the instructions in the blue box to get an LB and UB estimate like we did in class, replacing “inf” in the UB column (col. B) with 400 as an arbitrary upper bound. Compare your results here in 2-3 sentences.

    16. Using Carson et al. calculation and KMT lower bound calculation, the lower bound mean WTP is calculated to be $53.60, as indicated in Carson et al. paper (third paragraph on p. 272). The upper bound mean WTP is also calculated to be $102.70, which indicates that respondents are willing to pay any dollar amount ranging from $53.60 to $102.70 for an Exxon Valdez-type oil spell.

  16. Review the Living Roof survey posted in your iLearn block for Stated Preference. Reflecting on the survey and your analysis, explain what you think
    1. worked well in the survey and

      2. Overall, the survey was written in a very concise and reliable manner. Particularly, the question on the reasons why a respondent is not willing to pay for the project is very well-structured, as it helps separate ‘protest responses’ quite easily. Furthermore, the first three questions regarding environmental concern are also equally important, as these questions determine the behavioral patterns of the respondents, primarily unknown in this project.

    2. what do you think could be improved were you to repeat this project? In answering, take into consideration the selection of the population to be sampled noted at the top of the survey, and the survey instrument, such as description of goods provided, elicitation formats, framing, choice of bid levels, and possible bias at any point in the process.

      3. I think the choice of bid levels is a little higher for students and their parents. Most often, students are not willing to pay an additional amount, even if they believe that the deployed solution would be beneficial for them. A bid level ($30, $20, $40) would be much better to let low-income groups participate in the program.