# statistical assesment.

1. For this question you are required to use the European Social Survey (2011) Full dataset (with weighting) .Where appropriate, consider any transformations/recoding that might facilitate the analyses.
There would appear to be reasonable grounds for considering that personal happiness, general health and age might be related to each other. These are measured in the dataset, using the variables of ‘happiness’, ‘health’ and ‘agea’, respectively.
(a) Make a statistical assessment of each of these three variables independently
(b) Consider whether and in what way there is an association between any combination of two of the three variables.
(c) Draw a plausible causal diagram for the relationship between the three variables, justifying why you have drawn it in the way you do. (d) Analyse the causal diagram and explain what conclusions you can come to about the relationship between the three variables (e) What are the possible limitations of your model
2.For this question we use data from the Office for National Statistics’ 2005 Time Use Survey. This survey collects information on how much time people in Great Britain spend on different activities, such as sleeping and paid work.Table A6.1 below shows estimates, with their standard errors, of the mean number of minutes per day people in Great Britain spend on selected activities.
(a) How many minutes per day, on average, do women engage in paid work?
(b) What is the standard deviation of the sampling distribution for the average number of minutes women engage in paid work?
(c) State whether the sampling distribution for the average number of minutes men engage in paid work is more spread out or less spread out than the sampling distribution for the average number of minutes women engage in paid work [2 marks].Briefly explain how you know this
(d) Suppose that we double the number of men in our sample. Describe two ways in which this increase in sample size changes the sampling distribution for the average number of minutes men engage in paid work
(e) Let us say that we are interested in the relationship between the average number of minutes women spend on childcare (“caring for own children”) and the average number of minutes women spend on paid work. The correlation coefficient describing the relationship between these two variables is -.20 and its standard error is .04. However, the negative relationship between childcare and paid work may not entirely be due to the causal effect of childcare on paid work because of confounding variables.
a. Give one example of a possible confounding variable and explain why it might be a confounding variable
b. Now give one example of a possible intervening variable and explain why it might be an intervening variable.
(f) Now give one example of a possible instrumental variable and explain why it might be an instrumental variable
(g) Draw a causal diagram showing the relationship among the variables in terms of the minutes spent on childcare (‘X’), minutes spent on paid work (‘Y’), the confounding variable from (i) (‘Z’), the intervening variable from (ii) (‘A’), and the instrumental variable from (iii) (‘B’) [5 marks].
(h) Given the causal diagram in (f) and thinking about the different strategies for estimating causal effects, give two examples of different approaches that could be used for estimating the causal effect of the variable minutes spent on childcare (‘X’) on the variable minutes spent on paid work (‘Y’).
3. In 1974, in his seminal piece , Richard Easterlin argued that increasing average income did not raise average well-being, a claim that became known as the Easterlin Paradox. However, in recent years many different studies have provided empirical evidence against the Easterlin’s Paradox. Some researchers, on the other hand, have argued for a modified version of Easterlin’s hypothesis: the link between income and well-being exists only among those whose basic needs have not been met, and beyond a certain income threshold, further income is unrelated to well-being.
We can talk about two different versions of this revised Easterlin hypothesis:
1- Beyond some level of basic needs, income is uncorrelated with well-being. (Stronger version)
2- The magnitude of the effect of income on subjective well-being estimated among the poor significantlydiffers from that found among the rich. (Weaker version)
In this exercise, you are asked to test these two versions using the dataset ‘Easterlin.csv’ , and by estimating the following linear equation :
where:
• c denotes country
• I denotes the indicator function
• GPD is the gross-domestic product per capita
• t denotes to the income cut-off point between the poor and the rich
• ε denotes the error term
Do the analyses for the three different years available in the dataset for each of three different income cut-off points: 8000, 15000 and 25000.
(a) Briefly explain all SPSS steps involved and provide relevant outputs
(b)Provide interpretations of your model findings and explain why your findings do or do not.

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