Social Statistics ICA Assignment Coursework Example

Social Statistics ICA Assignment
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Social Statistics ICA Assignment
Question 1
Part A. Part B.
Total Eligible voters =5,000 people
Single Random sample =250 people
Non responders=50, responders=200
Yes [leave]= 97, No [remain]= 103
UK leave EU 52 of voters, Remain 48 percent of Voters
Proportion of p̂= 97
200
= 0.485
Estimated standard error (e.s.e)
= p 1- p1-f√(n-1)N=5000, n=250, f=n/N=250/5000=0.05
= 0.485 1- 0.4851-0.05√(250-1)=0.03087095% confidence for p̂ is given by
[p̂ – 1.96(e.s.e), p̂ + 1.96(e.s.e)]
=[0.485 – 1.96(0.030870), 0.485 + 1.96(0.03070)]
=[0.4244948, 0.5455052]
For the respondents actually voted
p̂ is the proportion of respondents who actually voted.
N=5000, n=250, f=n/N=250/5000=0.05
136 respondents voted leave [YES]
114 NO
p̂=136250=0.544estimated standard error (e.s.e) of p̂ is
= 0.544 1- 0.5441-0.05250-1=0.03076495% confidence interval given as [p̂ – 1.96(e.s.e), p̂ + 1.96(e.s.e)]
=[0.544 – 1.96(0.030764), 0.544 + 1.96(0.030764)]
[0.48370256, 0.60429744]

Part C.
The confidence interval range of the proportion of respondents who actually voted leave (non-responders included) is larger than the confidence interval range of the proportion of respondents who strictly responded leave (non-responders excluded). Most of the non-responders as indicated in the survey actually voted leave at the end. The confidence interval range of the true proportion who voted leave [0.4244948, 0.5455052] indicates the voting situation will be above 40%, but below 52%.

This C.I range is close to the real situation where 52% of voters wanted UK to leave EU in the final results.
Part D
Proportion of non-respondents amongst those who actually voted to leave
p=50136=0.367647Proportion of non-respondents amongst those who actually voted to leavep=50114=0.438596H0: N.A is independent of an individual’s actual vote.
H1: N.A is not independent of an individual’s actual vote.
5% significance level
95% Confidence Level
YES NO TOTAL
N.A 38 12 50
Actual Vote 136 114 250
TOTAL 174 126 300
Expected counts=Row total x column totalsample sizeYES NO
N.A 50 x 174300=2950 x 126300=21Actual vote 250 x 174300=145250 x 126300=105 x2=38-29292+ 12-21212+136-1451452+114-1051052=7.980296 P.o.f = (2 -1)(2-1)=1
p ≤0.01, therefore, p ≤ 0.05,
Conclusion: Reject Null Hypothesis
7.980296  > 0.05, indicating that missing responses are independent of an individual’s actual vote. Majority of the people in the missing responses voted “leave” although the survey results do not recognize them as leave votes.
Part E
Two other forms of bias in a survey conducted by telephone may include:
Researcher bias (experimental bias). Researchers can be biased especially in the manner in which they word their survey questions. This often happens when a researcher in a telephone wants the results to portray his or personal stance.
Coverage errors. These could lead to area selection bias in the survey samples especially for respondents in differing UK regions but lacks telephone or landline contacts. There is high probability that such respondents missed being included in the samples
Question 2:
Suitable Research Objectives
Confusion has arisen as to whether the United Kingdom should exit or remain in the European Union. Predicting the proportion of voters who will vote Remain and of those will vote Leave is a little confusing since voting intentions will not follow party lines. For a polling company wishing to perform a national survey to predict the likely proportions of leave and remain, voters, suitable research objective can as follows,
To determine the likely proportions of Remain and Leave voters in the upcoming referendum on UK membership of the European Union.
To know whether or not voting intentions may differ according to a variety of demographic factors (like age, gender, a region of the UK, and socio-economic status among others.
Target population
The United Kingdom is a country with diverse ethnic groups, societies, and individuals from different states. The population is extremely large for a simple survey. Concerning voting intentions in the upcoming EU referendum, target population should be all eligible the voters. Therefore, to determine the eligibility of the population to vote, people or respondents to be considered are supposed to have an age limit of 18 years and above, and belong to, at least one of the following groups:
A British native living abroad who has been enlisted to vote in the UK in the most recent 15 years.
A British or Irish national living in the UK
A Commonwealth resident living in the UK and has leave to stay in the UK or one who does not oblige leave to stay in the UK
An Irish citizen living abroad but was born and has been enrolled to cast their ballots in Northern Ireland in the most recent 15 years
Sampling frame
For the company to clearly generate datasets and address the research objectives, it has to identify source materials or devices from which samples will be drawn. These may include all individuals, households or institutions within UK population that are relevant to the referendum polls and can be sampled. For the purpose of this research, the first sample frame worth considering is the list of all eligible voters accompanied with their phone numbers. However, considering that the UK is such a big nation with a large population, obtaining such a list may sometimes be difficult, resorting to a Random Digital Sampling in which a computer retrieves random phone numbers from well-known area codes and prefixes can be a brilliant idea. The researcher can then use these numbers without bias since every phone number will have an equal probability of selection.
When calling these numbers, the interviewer needs to determine the number of adults living in that household; this identifies with the likelihood of selection of any person. A grown-up living alone has a likelihood of 1.0 of being confronted for an interview; an adult living with another adult, however, the probability of being interviewed is 0.5. This individual ought to be chosen at random to avoid bias, and there are an assortment of approaches to do this (frequently the “most recent birthday” technique is utilized). Despite the fact that every household unit has a similar probability of being chosen, the individual respondents in the survey do not. That relies on how extensive the house is and what number of phone numbers come into the data house.
Survey Design, Questioning and Measurement methods
There are several methods for administering or overseeing an opinion poll study that the company may be obliged to consider, for example, direct phone call, street intercept surveys, use of emails, online studies, and individual in-home surveys. A survey normally comprises of various inquiries that respondents answer in a set format. Typically, there are closed-ended and open-ended questions. The company may choose to use open-ended questions when requesting the public opinion through phone calls since these questions give respondents a chance shape their own answers. For an online survey or face-to-face interviews, closed-ended questions which only gives the respondents a chance the pick an answer from a given a choice would be the best. To ensure efficient and effective feedback, the questions have to be short and clear. With the closed-ended, questions, the answer format should be in the form “Yes,” “No,” or “None” to represent “leave,” “Remain,” and “undecided or non-response” respectively.
Sample Questions
Below are some of the survey questions the company might useful.
Are you
Male
Female
Age
Above 18
Below 18
Are you a citizen of United Kingdom?
Yes
No
Where is your current residence?_______(fill).
What is your main source of income?
__________(fill).
Should the United Kingdom leave the European Union?
Yes
No
None
Nonresponse
The non-respondents proportion represents those who did not contribute at all, probably, because they were undecided or the researcher was unable to reach them. These people are key components of the sample population and are, as well, representative of a sect of the public opinion. Hence must be included when calculating and interpreting sample proportions.
Survey Results
A good survey report should be accurate and free of errors in addition to presenting clear findings with strong conclusions. Basically, its structure follows the convenience of the target population. For this survey, the target population is that of eligible voters in the forthcoming EU referendum polls. For the company to ensure effective outreach, they should consider structuring the results according to the goals of the survey, rather than by question order and display them on mass media platforms like Televisions. Meaning, the researcher ought to look back at the objectives and ascertain that all of them are covered. To ensure that both statistical and practical significance the survey data are met, the results can be summarized in the form of graphs, table, or charts presenting proportional percentages. That is the percentage proportions of those who are likely to vote “leave,” those who are for the “Remain” option, and those who are likely to remain undecided or not vote all.