Reference no: EM133088059

Quantitative Data Analysis

Aim:

To reinforce understanding of quantitative data analysis skills and knowledge, including understanding the different types of data, the use of graphs and summary statistics to support exploratory data analysis, and hypothesis testing.

Part A: Exploratory Data Analysis

Question 1
Psychologists asked 46 golfers (Psychonomic Bulletin & Review, 2008), after they played a round, to estimate the diameter of the hole on the green by visually selecting one of nine holes cut in a board. The researchers compared their total score (adjusted for handicap) to the estimated diameter of the hole for each golfer. They wanted to see if there was a correlation between performance and perceived size of the holes.
a) What is the experimental unit in this experiment?
b) Specify the two variables measured in this experiment.
c) For each variable, write down whether it is categorical or numerical.
d) For any numerical variables, identify whether they are discrete or continuous.
e) Which variable is the response variable and the explanatory variable?
f) What graph could be drawn to compare the two variables?
g) Would you expect a positive or negative relationship between the two variables?

Question 2
For each of the following variables, indicate whether they are categorical or numerical. Also, write down what type of graph can be drawn for each.
a) Whether the person has ever been a victim of crime.
b) Age of place of residence (in years)

Question 3
For each pair of variables, specify which variable is the explanatory variable and which is the response variable. Also identify whether the variable is categorical or numerical.
a) A person's weight and blood pressure
b) A person's IQ level and gender
c) Whether or not a person is the first born in a family and whether or not they are an introvert.

Question 4
For each of the pair of variables in Question 3 above, write down the type of graph that you could draw to visually depict any relationships.

Question 5
The following images show graphs which are misleading or poorly designed. For each graph, critique its design and explain how it could be improved to better represent the data.

Question 6
The weights of 8 new-born dolphins (kg) are shown below:
16.1, 17.9, 16.4, 16.0, 17.0, 18.1, 17.1, 17.4
Manually calculate the following descriptive statistics:
a) Mean
b) Median
c) Variance
d) Standard deviation

Part B: Hypothesis Testing

Question 7
For each of the following scenarios, identify whether it would call for one-sample or two-sample hypothesis testing. If the latter, does the scenario involved paired or independent samples?

a) The hypothesis is that programmers trained in Java will take longer to complete a training course to teach them Python than will programmers who were originally trained in C++. We have gathered data from 20 Java programmers and 20 C++ programmers.

b) The hypothesis is that companies who invest in new IT infrastructure will receive an average return on investment of at least 150% over the next 5 years. We have data gathered from the records of 50 companies.

c) The hypothesis is that using a fitness app on their smart-phone will help people to lose weight. We have measurements of the initial weight for 50 individuals, and also of their final weight after using the app for 2 months.

Part B: Hypothesis Testing

Question 7
For each of the following scenarios, identify whether it would call for one-sample or two-sample hypothesis testing. If the latter, does the scenario involved paired or independent samples?

a) The hypothesis is that programmers trained in Java will take longer to complete a training course to teach them Python than will programmers who were originally trained in C++. We have gathered data from 20 Java programmers and 20 C++ programmers.

b) The hypothesis is that companies who invest in new IT infrastructure will receive an average return on investment of at least 150% over the next 5 years. We have data gathered from the records of 50 companies.

c) The hypothesis is that using a fitness app on their smart-phone will help people to lose weight. We have measurements of the initial weight for 50 individuals, and also of their final weight after using the app for 2 months.

Question 8

As discussed in lectures p-hacking is an inappropriate approach to research, in which the choice of hypothesis is made after data-gathering and analysis. The following online exercise illustrates the problems of p-hacking, showing how two contradictory hypotheses can both be found to be supported by the same data-set, by altering the variables used in the analysis. Experiment with the settings on this example. First try to show that Democratic governments have a negative impact on the economy, and then see if you can produce evidence to support the opposite hypothesis.

Attachment:- Quantitative Data Analysis.rar