Example of an exam assignment

The slides below show you what you can expect on an exam based on the material of the past weeks.

Please note that:

  • these examples exaggerated the complexity of the exam.

Definition question

Answer two questions from the list below:

  • What measures of central tendency are most commonly applied in social sciences?

  • What are extreme observations or outliers?

  • What effect do outliers/extreme observations have on the mean/median, standard deviation/IQR?

  • Is the median one of the quantiles or is it a measure of central tendency?

  • What is the Hypothesis Testing?

Problem introduction

An RCT experiment was designed to understand the effect of technology (“Minimal” vs “Optimal”) on rice yields. It included:

  1. Randomly selecting 60 farms and offering them two equivalent rice varieties to plant.

    • each farmer picked one variety randomly.

  2. Training half of them in applying Optimal technology (treatment), and

  3. Keeping half of the farmers with the same minimal technology (control).

During the production season, researchers recorded for each farm:

  • Technology, rice variety, rice yield, and fertilizer use.

  • The research objective was to measure the effect of technology on rice yield.

Answer the questions on the following slides based on this example.

Descriptive analysis (1)

Continuous variables

Unique Missing Pct. Mean SD Min Median Max
yield 60 0 5.4 1.1 3.1 5.4 7.9
nitrogen 52 0 77.3 49.6 0.0 79.0 148.6
potassium 60 0 33.1 15.1 1.7 34.3 61.4
phosphorus 60 0 37.6 21.6 0.8 38.8 74.7

Categorical variables

N %
tech Minimum (control) 30 50.0
Optimum (treatment) 30 50.0
variety V1 30 50.0
V2 30 50.0

Checks and Balances (1)

  • What differences do you observe between technologies in terms of the fertilizers used?

  • What can we conclude about the quality of random assignment based on this plot?

Checks and Balances (2)

Minimum (control) (N=30)
Optimum (treatment) (N=30)
Mean Std. Dev. Mean Std. Dev.
nitrogen 77.7 50.4 76.9 49.7
potassium 28.0 14.4 38.2 14.2
phosphorus 31.7 17.9 43.4 23.7

Significance levels are: ‘+’=.1, ‘*’=.05, ‘**’=.01, ‘***’=0.001

  • Perform hypothesis testing about the difference in mean fertilizer application between the two technologies.

  • What can we conclude about the quality of random assignment based on this table?

Effect of technology on yields

  • Our key objective is to quantify the effect of technology on yields.

  • What differences do you observe between technologies in terms of rice yields?

  • Can we conclude about the causal effect of technologies based on this plot?

HT: effect of technology on yields

Minimum (control) (N=30)
Optimum (treatment) (N=30)
Mean Std. Dev. Mean Std. Dev.
yield 5.2 1.1 5.6 1.1

Significance levels are: ‘+’=.1, ‘*’=.05, ‘**’=.01, ‘***’=0.001

  • Why do we need this HT?

  • Formulate H0 and H1.

  • Conclude about the effect of technology on yields.

  • What statistics did you use?

  • What is the highest level of significance for your results?

Conclude about the effect of technology on yields

  • Does the optimal technology have any causal effect on yields?

  • How large is this effect?

  • Does the RCT performed here ensures the ceteris paribus?

  • What else can influence the effect of technology on yield?

  • How can we control for it?

Differences in yields between varieties

  • What does this plot show?

  • Considering previous results, can we conclude about the quality of random assignment now?

  • Is there a causal effect of variety on yields, which effect is this?

HT: effect of variety on yields

V1 (N=30)
V2 (N=30)
Mean Std. Dev. Mean Std. Dev.
yield 4.7 0.8 6.1 0.9

Significance levels are: ‘+’=.1, ‘*’=.05, ‘**’=.01, ‘***’=0.001

  • Formulate H0 and H1.

  • Conclude about the yield difference between varieties.

  • Based on our sample, can we conclude that variety has a causal effect on yields?

  • Does our sample ensure the ceteris paribus? How does our sample ensure it?

Conclude again

  • Does the random assignment of technology ensure the ceteris paribus here?

  • What are the most relevant other factors that may influence the ceteris paribus in our sample?

  • Given that what can we conclude about the causal effect of technology on yields?

  • After today’s lecture you should be able to answer the following:

    • Can we “control” the effects of the other factors?

    • What econometric method can we use to re-establish the ceteris paribus?

    • How (can we at all) measure the effects of other factors such as fertilizer application on the yields?

How to measure the effect of nitrogen fertilizer on yield?

Framework for interpreting any statistical test

For your reference and information.

The keywords/concepts below are meant to improve the clarity of communication when performing the hypothesis testing. Please use it! They will help make your results understandable for the reader.

  1. Test name and what it is about (t-test about means comparison between two groups).

  2. \(H_0\) and \(H_1\).

  3. Estimated parameters (means, coefficients, differences, standard error), \(df\) / n observations.

  4. Level of significance of the HT. (\(\alpha = 0.05\) or 5% level of significance)

  5. Rejection rule: \(\text{p-value} < \alpha\) or \(|t| < c_{df, \, 1 - \alpha /2}\) (statistics vs critical value) or \(1 - \alpha\) confidence intervals (95% CI).

  6. Conclusions: reject/fail to reject;

  7. Implications

    • what do these conclusions imply for your analysis?

    • (for example. … reject \(H_0\). Thus, the mean “outcome” in the treatment group XX is higher than that in the control group, suggesting about the great success of our intervention …).