Statistical Report: Statistical Analysis of Irish Census Data Report

This report presents a statistical analysis of data from the 2011 Census of Ireland, focusing on non-normal data using various non-parametric statistical tests. The assignment requires the student to prepare a statistical report based on the provided data file, including descriptive statistics, tests for normality, and tests such as Mann-Whitney U and Kruskal-Wallis. The report emphasizes the importance of hypothesis testing, justification of significance levels, and clear reporting and explanation of results. Visual representations of data, such as Q-Q plots, box plots, and histograms, are also expected. The report follows the 8 Simple Rules procedure for computing a test statistic, ensuring a comprehensive and well-structured analysis of the data. The student must also explain and justify the statistical tests used, state assumptions, and adhere to a word count between 1,200 and 1,500 words, excluding supporting materials.

In this assignment you will use statistical tests for non-normal data. You may use
methods (non-parametric statistics tests) and tools (R, Excel, or SPSS) of your own
choice - please don't rely on one tool or method, variety is expected. It is not
necessary to replicate any test you carry out, ie if you perform a test in R it is not
necessary to repeat in SPSS and/or Excel. A data file (from the 2011 Census of
Ireland) is suggested, though students are permitted to choose a different file if
they wish (subject to approval by Dr O'Loughlin). Your task is to prepare a
statistical report based on the data in the file.
UPDATE LINK:
The Central Statistics Office provides data on "Small Area Population Statistics" –
see:
http://airo.maynoothuniversity.ie/files/dDATASTORE/small_areas/
theme_11_small_areas.csv
This CSV file has 18,488 records based on 68 columns of data. You are not
expected to use all the data in the file and you may reduce to eliminate unused
data if you wish. As there are a lot of data in this file, please be careful on what
you decide to report on - it is up to you to choose.
Some suggested reports:
 a comparison of methods of transport to work by County/Planning Region
 difference between different methods of transport in urban vs rural areas
 a comparison of journey times to work by County/Planning Region
 a comparison of time leaving home to travel to work by County/Planning
Region
 Correlations may also be tested
Suggested statistical tests:
 Descriptive statistics for all data used
 Tests for normality such Q-Q plots, Kolmogorov-Smirnov (please note - the
Shapiro-Wilk test does not work for sample sizes over 5,000)
 Mann-Whitney U Test/Wilcoxon Rank Test to compare two samples (eg -
travel times for Kerry vs Cork)
 Kruskal-Wallis H Test to compare three or more samples
 Post-hoc tests where appropriate
Suggested visual representation of data
 Q-Q/P-P plots

 Residuals
 Box plots
 Frequency Distributions/Histograms
 Scatter plots
Be aware that this is a statistical report and that Null/Alternate hypotheses,
justification of levels of significance, correct reporting of results, and explanations
of results are expected (see 8 Simple Rules procedure below). Please also explain
and justify any statistical test used. State clearly any assumptions made.
Word count should not be less than 1,200 or more than 1,500 words. This does
not include: data, code, tables, diagrams/charts, bibliography, tables of content,
quotations, or appendices. Please indicate on your cover page the word count.
Submit only one report document (Word or PDF) - support files such as R code,
SPSS outputs, Excel files, are not required.
8 Simple Rules
Based on Salkind (2014)
Follow these rules when computing a test statistic:
1. State the Null and Alternate hypotheses
2. Set the level of significance, eg α = 0.05
3. Select the appropriate test statistic (eg z, t, F, χ2, r)
4. Compute the test statistic value using appropriate formulas
5. Determine the degrees of freedom
6. Report result, eg t(49) = 4.75, p < 0.05
7. Determine critical value needed to reject Null hypothesis
8. Make a decision (reject Null in favour of Alternate hypothesis or fail to
reject Null hypothesis)
In most cases you will be asked explain what your result means. Your
conclusion should be based on the outcome of your statistical test. Simply
stating that your conclusion is “I reject the Null hypothesis” is an insufficient
explanation of the result. You should outline clearly what the result means and
use a diagram of an appropriate distribution to help explain your result.