Reference no: EM133027379

GV903 Advanced Research Methods - University of Essex

1 Tenure-track applications

Consider the following fictitious scenario: The job market for academics on Academic Island has been getting tighter. Each year, 3,000 new PhDs flood the market, but there are only 165 tenure-track positions available. The probability of getting a tenure-track offer per application is 0.012. Assume that there is no a priori knowledge about differences in ability or performance between the graduates, hence the same probability applies to all applicants per application.

Imagine you are one of those PhD students.

1. How many tenure-track offers do you expect to secure if you apply to all open positions in a given year?[6 points]

2. How many applications do you expect to write to secure your first offer?[6 points]

3. How many applications do you expect to write to secure three tenure-track job offers?[6 points]

4. What is the probability that you get between 4 and 6 offers if you send out all 165 applications?[6 points]

5. What is the probability that you end up without a job after 165 applications? [6 points]

6. If you want to make 90 per cent sure that you get a position, how many applications do you have to write?

Show the solutions using equations where feasible; insert the respective numbers, and write a brief explanation. Where feasible, write an R function that can compute the result using arbitrary parameters (instead of the numbers given above). In the bodies of the functions you write, use functions from only the base package. (I. e., do not use existing distribution functions.) Show that your functions work using the parameters from the respective task.

In Task 2.4, you compared a single data point for Essex to the distribution of changes among all other universities. However, we assumed that each university constituted a single data point. In making that assumption, any particular student's response at a small university was several times as important as any particular student's response at a large university. It would be better if we had the raw individual responses for all respondents from all universities to draw the exact empirical distribution of how satisfied customers were.

The OfS does not release disaggregated data. But we can use our knowledge of distributions to simulate the complete disaggregated dataset of responses. Follow these steps:

1. For each university in the nss-uni.csv dataset, create two normal (or bino- mial) distributions (for the two years) using the respective percentages and numbers of respondents per university and year.

2. Sample as many values from the distribution for 2020 as there are respondents in 2021, for each university.

3. Sample as many values from the distribution for 2021 as there are respondents in 2021, for each university.

4. Compute the pair-wise differences between 2020 and 2021 for each sampled observation, and save the differences in a new vector. This vector of sampled differences will be almost as good as the full, disaggregated dataset the OfS is not providing.

5. Now compare the simulated distribution for Essex respondents to the sim- ulated distribution for all non-Essex respondents, and revisit the question whether student satisfaction at Essex declined more than at other universi- ties, this time taking into account the full distributions of responses.

Attachment:- Advanced Research Methods.rar