Sampling and Chi-Square Test: Statistical Analysis of Fear of Flying

This report presents a statistical analysis of sampling techniques and hypothesis testing. It begins by outlining the appropriate sampling strategy for a study on the fear of flying within the UK population, emphasizing the use of stratified random sampling to account for demographic variations such as gender and age. The report then details the application of a chi-square test to determine if the type of aircraft influences simulator sickness. It includes the manual computation of the chi-square statistic, the formulation of null and alternative hypotheses, and the determination of the p-value. The analysis concludes that there is a statistically significant relationship between the type of aircraft and simulator sickness, though the effect size is small. The report references relevant literature to support the methodologies and findings.

STATISTICS
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Introduction
The objective of this report is to present the suitable sampling strategy and approach to obtain
an unbiased sample considering that key demographic attributes tend to influence the fear of
flight which tends to vary across regions. Also, using hypothesis testing another objective is
to highlight if the type of aircraft influences the simulator sickness.
Sampling
(a) The key objective is to select a representative sample of the UK population as a whole so
that the national figure with regards to fear may be estimated. It is known that the fear is
dependent on two demographic aspects namely the gender and age (bands of 10). To begin
with, it is imperative that the appropriate sampling strategy must be probability based which
allows for a random sample. However, owing to significant variation across key demographic
factors, a simple random sample would not be the appropriate choice. Instead, the stratified
random sampling technique would be the appropriate choice (Flick, 2015). This is because
the sample would be representative of the underlying population whether at the national level
or the regional or community level since the key attributes i.e. gender and age would be
rightly expressed and lead to lowering of bias thereby enhancing reliability of results
obtained from sample (Eriksson and Kovalainen, 2015).
(b) Consider the regional differences, it would make sense that the underlying sample should
comprise of these regional groups in the same ratio as their respective contribution to the UK
population. Also, for each of these regional groups, it would be pivotal and the distribution of
gender and age should be carefully monitored and thereby close to the actual representation
in the regional population (Hillier, 2016). This would ensure that every region is correctly
represented both internally and also in the UK population. It is likely that this would yield
reliable results.
Chi-Square Hypothesis Test
(a) The manual computation of chi square statistics is indicated below.
Observed frequency
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Expected frequency
Chi square calculation
χ 2=Σ ( O−E ) 2
E
χ 2= ( 34.34−30 )2
34.34 + ( 7.66−12 )2
7.66 + ( 86.66−91 )2
91 + ( 19.34−15 )2
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χ 2=0.5480+ 2.4558+0.2171+0.9731=4.1940
(b) The requisite hypotheses are as stated below.
 Null and alternative hypotheses
Null hypothesis H0: There is no effect of the type of aircraft flown with regards to the
simulator sickness.
Alternative hypothesis H1: There is significant effect of the type of aircraft flown with
regards to the simulator sickness.
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 Significance level
alpha=0.05
 Chi-square statistic computed =4.194
Degree of freedom
dof = ( r−1 ) ( c−1 ) = ( 2−1 ) ( 2−1 ) =1
 The p value
The p value for chi square statistic and degree of freedom comes out to be 0.0406.
 Result
It can be seen from the above analysis that p value is lower than significance level and hence,
sufficient evidence is present to reject the null hypothesis and to accept the alternative
hypothesis (Hair et. al., 2015). Therefore, the conclusion can be drawn that there is effect of
the type of aircraft flown on the simulator sickness.
 Estimate of effect size
Cramer’s phi (Cramer’s Φ or Cramer’s V) would be taken into consideration to comment on
the effect size.
Now,
(Row – 1) = (2-1) =1, (Column – 1) = (2-1) =1
dfsmaller = 1
Cramer ’ s Φ= √ 4.1940
148∗1 =0.1683
This indicates a small effect size.
Conclusion
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Based on the above, it can be concluded that stratified random sampling would be the
appropriate sampling strategy. Further, the sample selected would be unbiased if the key
attributed in each regional group is represented correctly and each regional group has a
proportional representation in the UK population. The chi-square hypothesis testing
highlights that simulator sickness is impacted by the type of aircraft.
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References
Eriksson, P and Kovalainen, A. (2015). Quantitative methods in business research (3rd ed.).
London: Sage Publications, p. 63-64
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research
project (4th ed.). New York: Sage Publications, p. 87-88
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P. and Page, M. J. (2015). Essentials
of business research methods (2nd ed.). New York: Routledge, p.98
Hillier, F. (2016). Introduction to Operations Research. (6th ed.). New York: McGraw Hill
Publications, p.104
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