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  2. Pick the 2 appropriate summary statistics you should report regarding the reaction time of the sample of the Roberton people who are aged 6 – 80 years? Select one or more

Pick the 2 appropriate summary statistics you should report regarding the reaction time of the sample of the Roberton people who are aged 6 – 80 years? Select one or more

Assessment 3: Public Health Data Analysis

The slogan for World Health Day 2004 – Road Safety Is No Accident – suggests that road safety does not happen accidentally, but requires a deliberate effort by governments and their many partners.

The WHO strategy for road traffic injury prevention has three objectives:

  • To build better systems for gathering and reporting data on traffic injuries;
  • To make prevention of road traffic injuries a public health priority in all countries;
  • To advocate for prevention and promote appropriate prevention strategies for road traffic injuries.

In Australia, on average, five peoples die every day in road crashes. In a 2018 report by the ABC using national data found that:

  • 48,592 people have died on the Australia’s road since 1989
  • Traffic injury is the biggest killer of children under 15
  • Traffic injury is the 2ndbiggest killer of Australians aged between 15-24
  • The yearly death toll has decreased from 3798 (1970) to 1225 (2017)

According to the AIHW Injury in Australia: transport accidents report (updated 9 Dec 2021), in 2018-19, transport injuries resulted in:

  • 63,900 hospitalisations (255 per 100,000 population) – 10 % of injury hospitalisations
  • 1,400 deaths (5.6 per 100,000 population) – 10 % of injury deaths

This is despite Australia’s strong legislative approach to road safety. Public health experts know:

  • Road deaths are predictable and preventable
  • Road safety is no accident

Links:

  • http://www.emro.who.int/violence-injuries-disabilities/violence-events/whd2004.html
  • https://www.abc.net.au/news/2018-01-25/every-road-death-in-australia-since-1989/9353794  https://www.aihw.gov.au/reports/injury/transport-accidents

 

Dataset: The Council of Roberton  

The Council of Roberton is interested in investigating risk factors that can lead to road accidents in their population. They have sent out a tender for the brightest researchers to inform their future public health policies and health promotion interventions. They are interested in the association between physical activity in terms of reaction time for stopping a car and preventing an accident.

The good news is that they have existing historical data. The data was collected from a census index from the Council of Roberton which has 17,935 residents aged between 6 years to 80 years.  Each individual’s data were identified by a six-letter identification code. From the records given on Moodle in the Excel file “Roberton Dataset.xlsx”, the age group and gender of each person in this population are known. Gender was only collected as a binary variable: Male and Female.  This data is a snapshot in time and there is no historical or post-research data available.

The Council wanted to examine the association between reaction time and physical activity. Therefore, they have conducted a one-off test as part of their health assessments and collected the reaction time of the individuals.  A quick reaction time on the test is considered an indicator of a good ability when to stop a car.

 

 

A stratified random sample of 100 Roberton residents has been obtained. The stratification was based on the age groups and the sample size from each stratum was in proportion to that in the population:

 Age Group  6-20  21-35  36-50  51-65  65-80
 %  22  23  25  19  11

 

 Variable  Descriptor
 Age  Years (recorded as the date of birth)
 Gender  Male (M) and Female (F)
 Handedness  Left-Handed (LH) and Right Handed (RH)
 Physical activity  Hours per week
 Reaction time to test  Seconds
 Reaction time: Slow and Quick  Slow (>= 0.31 sec) & Quick (<0.31 sec)

 

DATASET:

Volunteer ID Age Gender Handedness Phys. Act. Reac. Time Reacton time: slow vs quick
1 IHVDDL 26 M RH 3.5 0.254074 Quick
2 NCMEOX 43 F RH 1.5 0.390774 Slow
3 SBRHPO 44 M RH 4 0.300103 Quick
4 LVCZRF 64 M RH 3 0.415153 Slow
5 XTVSFC 20 M RH 4.5 0.250908 Quick
6 XDRZKO 28 F RH 3 0.328946 Slow
7 MBNMJB 58 F RH 3.5 0.327346 Slow
8 CUOMNB 52 F RH 3.5 0.323848 Slow
9 OZHARU 19 M RH 6 0.250345 Quick
10 DEKZIA 51 F RH 3 0.364936 Slow
11 SGBVTW 43 M LH 4 0.263651 Quick
12 ZEMJFK 43 F RH 3 0.349891 Slow
13 QKAZUL 35 M LH 5 0.226787 Quick
14 VNJVGG 19 M RH 5 0.202515 Quick
15 CSRNFW 44 M RH 4 0.322696 Slow
16 IEFZGB 15 F RH 4 0.294385 Quick
17 LZSUZN 14 M LH 4 0.201525 Quick
18 WUQKQT 10 F RH 4 0.276566 Quick
19 PNEKWX 28 M RH 3 0.273305 Quick
20 TUWUIB 52 M RH 2 0.335039 Slow
21 HTYTIZ 74 M RH 2 0.406903 Slow
22 CQBIEK 30 F RH 4 0.308271 Quick
23 NTTIWH 80 F RH 3 0.408785 Slow
24 MBEVBF 9 M RH 5.5 0.228226 Quick
25 SXFIOZ 19 F RH 3.5 0.235167 Quick
26 MMDHJO 40 F RH 2 0.373712 Slow
27 XTJTWD 32 M RH 5 0.236355 Quick
28 MQKEOV 41 F RH 3 0.330303 Slow
29 MOULBE 38 M RH 3 0.342959 Slow
30 AVQKZS 14 M RH 5 0.227944 Quick
31 FFLNML 64 F RH 3 0.402127 Slow
32 DIGFUL 29 F LH 3.5 0.245797 Quick
33 YTNIEZ 47 F RH 1.5 0.336358 Slow
34 SFKMGD 11 F RH 4 0.215319 Quick
35 HEUUNJ 63 M RH 2.5 0.34338 Slow
36 NEGDOQ 34 F RH 3.5 0.265359 Quick
37 BSVYMI 9 M RH 4.5 0.233361 Quick
38 IJFHLS 58 M RH 1.5 0.349041 Slow
39 FESBNT 47 M RH 2.5 0.3884 Slow
40 CNHEMA 65 M RH 2 0.430545 Slow
41 CWZNLS 39 M RH 2 0.354201 Slow
42 QPMVUT 38 M RH 3.5 0.296223 Quick
43 PTJFWW 56 F RH 2.5 0.411136 Slow
44 LLZBOA 58 M RH 2 0.415038 Slow
45 GJUVFI 43 M RH 3 0.324668 Slow
46 QYBTNW 45 F RH 1.5 0.345047 Slow
47 AAIRSA 27 F RH 3 0.289131 Quick
48 JQEXEC 17 M RH 4.5 0.204639 Quick
49 FRBPQZ 63 F RH 1 0.451813 Slow
50 XTWNSJ 13 M RH 6 0.209233 Quick
51 SONPZC 36 M RH 2.5 0.289609 Quick
52 IQNVAC 33 M RH 5 0.256971 Quick
53 MPOSOE 48 M RH 4 0.343136 Slow
54 GBHCDK 14 M RH 5.5 0.183928 Quick
55 UELXCD 52 F RH 2 0.397813 Slow
56 RAFLUQ 40 F RH 1.5 0.319358 Slow
57 MBJXYS 48 F RH 1.5 0.351163 Slow
58 UNMRHO 14 M RH 6 0.202551 Quick
59 PMYSPL 15 F RH 5 0.197103 Quick
60 ILJJMK 48 M RH 3 0.375297 Slow
61 QZROYJ 65 F RH 3.5 0.371229 Slow
62 VYJVHD 35 M RH 5 0.318889 Slow
63 QFUBQK 13 M RH 6 0.196339 Quick
64 LJOQYQ 69 F LH 0.5 0.378272 Slow
65 GMSRCA 73 M LH 1.5 0.368826 Slow
66 OMKDVR 37 F RH 2.5 0.366972 Slow
67 EBTOIJ 52 M RH 1.5 0.42042 Slow
68 TSUJEB 50 M RH 2.5 0.36039 Slow
69 IKAMON 9 F RH 5.5 0.176372 Quick
70 EMXRID 62 F RH 2.5 0.41135 Slow
71 OIXEFY 67 F RH 1 0.385949 Slow
72 ZPFUEX 11 F RH 3 0.294913 Quick
73 CFQFDJ 6 F LH 3.5 0.193657 Quick
74 QAJNNV 7 F RH 5 0.246434 Quick
75 ZPCLMA 27 F RH 3.5 0.316907 Slow
76 APWZDY 24 M LH 5 0.203713 Quick
77 KTDTFB 75 M RH 2 0.456536 Slow
78 GAAWQB 9 M LH 4.5 0.187153 Quick
79 DQYYAW 18 M RH 4.5 0.268085 Quick
80 CZOKCZ 66 M RH 0.5 0.411091 Slow
81 YLBHXJ 8 M RH 6 0.16851 Quick
82 EIOHUL 9 F RH 3 0.26532 Quick
83 ZKUZLC 14 F RH 4 0.212277 Quick
84 ASQWBJ 71 M RH 0.5 0.415695 Slow
85 STPQKA 43 F RH 3 0.368288 Slow
86 JSPACY 31 F RH 2.5 0.278953 Quick
87 SLZNQC 12 F RH 3.5 0.222009 Quick
88 PRYMNW 55 F RH 2 0.365204 Slow
89 TIGFWA 32 M RH 5.5 0.229825 Quick
90 HFXUKA 43 F RH 2 0.381614 Slow
91 ZRBLZF 47 M RH 4 0.292199 Quick
92 DDOIWB 34 F LH 3 0.260509 Quick
93 EUJKGH 51 F RH 1 0.362534 Slow
94 KFWAMH 12 F RH 4.5 0.229808 Quick
95 VTRWSR 11 F RH 3 0.246107 Quick
96 PFAGGU 32 M LH 5 0.21584 Quick
97 LDTOBG 25 M RH 5 0.243748 Quick
98 KQDGMK 34 M RH 5.5 0.233727 Quick
99 SQLZZA 42 M RH 2.5 0.30988 Quick
100 RXQQHR 72 F RH 3 0.43385 Slow

 

Section A: Understanding the context (8 marks) 

The Council of Roberton is really concerned about the number of recent road accidents, and has called a community meeting.  They have called for an enquiry named the Roberton report. You are part of the team to help them make decisions for their community.  The aim of your assignment is to investigate injury prevention and road safety.

Let’s ask some preliminary questions about accidents.

Additional resources:

  • Stopping distances: speed and braking(graph)
  • Stopping distances on wet and dry roads(table)

 

  1. What factors may influence road safety and contribute to the road toll?

 

List 2 direct factors and 2 upstream factors.    (4 marks)

 

  1. A person’s reaction time can be critical to their safety.  Consider that you are driving a good car in dry conditions at 60 km/hr and a child unexpectedly steps out from behind a parked car which is only 45 meters in front of you.  Will you have enough time to stop?

 

Using the graph provided, state the distance travelled in meters if the car is travelling at 60 km/hr on a dry road.  (no units required)    (1 mark)

 

  1. Using the table provided, state the distance travelled in meters if the car is travelling at 100 km/hr on a dry road. (no units required)(1 mark)

 

  1. Now that we know that driver reaction distance in meters and car braking distance play a role in stopping a car.

 

Describe your findings of whether the car stopped at 60 km/hr or 100 km/hr for the child 45 m away by completing these two sentences:

o  At 60 km/hr, the car will … o  At 100 km/hr, the car will …                                  (2 marks)

 

 

Section B: Describing & Summarising Data (20.5 marks) 

It is important to have an understanding of your data and variables in research.

Before we start our analysis, we need to understand our population and the sampling methods used.  Then, before we do any statistical tests, we need to describe the data with descriptive statistics and graphs.

 

Resources: Please see the “Useful Assessment Resources” folder for a PDF of the questions in the quiz, as well as the “Formula Sheet & Tables” document.

 

  1. The Roberton sample was obtained by stratified random sampling with the strata based proportionally on age groups.  This type of sampling may be necessary for investigating the average reaction time.

 

What had to be known to achieve it? (Select 1 or more correct answers) [3 marks]

 

  • A sampling frame of the entire population, along with their age and the proportions of each sub-group in the population is needed to achieve this stratified sampling.
  • Age is not relevant to the condition investigated and therefore will have no effect on reaction time or cognition.
  • Stratified sampling allows for sequential order within the sample which ensures that the attribute studied is random.
  • Stratified sampling allows for the sampling to be random within each sub-group being investigated (in this case, each age group) – so the proportions of the different age groups are the same in the population and the sample.
  • Age is often referred to as “the universal confounder” – so reaction time might be affected by age.
  • A sampling frame which divides the population into a set of different coherent areas and randomly selects areas to assess.

 

  1. Create a table of variables by matching the type of data to each variable listed below.   [6 marks]
Variable Descriptors Type of Data
Age Years (recorded as the date of birth)  
Gender Male (M) and Female (F)  
Handedness Left Handed (LH) and Right Handed (RH)  
Physical activity Hours per week  
Reaction time Seconds  
Reaction time: Slow and Quick Slow (>= 0.31 sec) & Quick (<0.31 sec)  

 

  1. A graph is a really useful way to see how the data is distributed.

 

Therefore your next step is to:

Draw a graph of reaction time.

Please attach the graph as a file below.

In the text box, type the file name only.   [5 marks]

 

Answers to FAQ for this question:

  1. No other variables are required for this graph – only “reaction time”.
  2. Part of the purpose of this question is for you to figure out what type of graphis appropriate & then graph it.

 

  1. Time to identify the appropriate numerical summaries to describe the typical reaction time of individuals in Roberton.

What is the mean of the sample? (4 decimal places) [1 mark]

 

  1. What is the median of the sample? (4 decimal places)[1 mark]

 

  1. Indicate if this statement is True or Falsein regards to the graph and statistics obtained so far.

“The graph shows a fairly normal distribution, and the values of the mean & median are fairly similar.

Hence, the mean is an appropriate statistic to describe reaction time.”       [0.5 mark]

 

  1. Pick the 2 appropriate summary statistics you should report regarding the reaction time of the sample of the Roberton people who are aged 6 – 80 years? Select one or more: [2 marks]
    • Range
    • Mean
    • Inter-quartile range
    • Mode
    • Median
    • Standard deviation

 

  1. We need some more information to continue.

What is the reaction time range of your sample? (4 decimal places)  [1 mark]

 

  1. What is the reaction time standard deviation(SD) of your sample? (4 decimal places) [1 mark]

 

 

Section C: Describing & Summarising Data using Graphs and % (11 marks) 

Let’s have a closer look at some key variables: Gender and Reaction time: slow vs quick.

 

To answer this section, you’ll need to create a summary table that shows the frequency and percentages.

You’ll also need to create an appropriate graph & interpret your results.

  Slow n (%) Quick n (%) Total n (%)
Male      
Female      
Total      

 

  1. What overall outcome percentage should be calculated for this table? [1 mark]

 

Questions 15 to 19 below are (1 decimal place, no units required) format.

 

  1. What is the numerical value of the percentage identified above? [1 mark]
  2. What is the percentage in the “females – slow” box of your table?  [0.5 mark]
  3. What is the percentage in the “females – quick” box of your table? [0.5 mark]
  4. What is the percentage in the “males – slow” box of your table? [0.5 mark]
  5. What is the percentage in the “males – quick” box of your table? [0.5 mark]

 

  1. Graph the data from your table ofGender and Reaction time: slow and quick.

After creating your graph select the graph below which best represents your data. [1 mark]

 

  1. The graphs in the previous question are a good way to look at the data but are not complete.

 

How could you improve the graph in the question above? (Select all that apply) [3 marks]

  • It needs a more detailed title
  • Label the y-axis
  • Requires a legend
  • Legend requires more detail
  • Label the x-axis
  • It needs a shorter title

 

  1. Write a brief conclusion of Section C. [3 marks]

 

Section D: Conducting Statistical tests (25.5 marks) 

 

Great news, the Council of Roberton has found your preliminary results very valuable.

Now let’s do some statistical tests to investigate the data in more detail.

 

The first thing we’ll be looking at is: Do males and females differ in their reaction times?

 

Over the next few questions you will need to create a summary table and conduct a test of significance (95% CI and p-value) between the males and females to answer if there is a difference between their reaction times.  Follow all steps clearly and write a clear conclusion.

Hint: Let’s complete all the steps in hypothesis testing.

 

  1. State the Null & Alternative hypotheses [2 marks]

 

  1. For the following, match the assumption with how it is met in this test. [4 marks]

 

Distribution of data in each group:

Groups being compared are:

Patients within each group are:

Equality of group variance using Levenes (ratio) test:

 

  1. What is the reaction time mean for females? (4 decimal places) [1 mark]

 

  1. What is the reaction time standard deviation for females? (4 decimal places)  [1 mark]

 

  1. What is the reaction time meanfor males? (4 decimal places)  [1 mark]

 

  1. What is the reaction time standard deviationfor males? (4 decimal places)  [1 mark]

 

  1. Calculate the difference in means (Female – Male) (4 decimal places)[1 mark]

 

  1. Calculate standard error (SE) (4 decimal places)[2 marks]

 

  1. Calculate the degrees of freedom [1 mark]

 

  1. What is the T-multiplier? (2 decimal places)[1 mark]

Congratulations. You’ve now got the necessary statistics to calculate the p-value and 95%CI

 

  1. Calculate the T-statistic (2 decimal places). [1 mark]

 

  1. What is the p-value? [1 mark]

 

  1. Considering the p-value in the previous question, answer if the following statement regarding the pvalue is TRUE or FALSE?   [0.5 mark]

 

“As the p-value is > 0.05, the p-value is not significant. Therefore, in this sample we can not justify rejecting the null hypothesis.”

 

  1. What is the 95% Confidence Interval? (3 decimal places)[1 mark]

Hint: Write your answer as x.xxx to y.yyy, e.g. -0.123 to 1.234

 

  1. The correct description and interpretation of your 95% Confidence Interval is:   [3 marks]

 

  1. Write a conclusion paragraph about your statistical conclusions for Section D. [4 points, 1 mark each = 4 marks]

 

 

 

Section E: Interpreting statistical test results (13 marks) 

Now, let’s look at the relationship between handedness and reaction time: slow vs quick.

Hint: For this question, you’ll need your data summarised in the table below.

  Slow Quick Total
Left      
Right      
Total      

 

  1. For the relationship between Handedness (left) and Reaction time (slow) calculate the Odds Ratio (2 decimal places).  [1 mark]

 

  1. For the relationship between Handedness (left) and Reaction time (slow): interpret the results of the odds ratio from the previous question [2 marks]

 

 

Next, you will calculate the SE and 95% CI of the Odds Ratio, and interpret the 95% CI.

You will need your odds ratio (handedness (left) and reaction time (slow)) from the earlier question to 6 decimal places.

 

  1. Calculate the standard error of the odds ratio: (4 decimal places)[1 mark]

 

  1. Calculate 95% CI of the Odds Ratio. (3 decimal places)[1 mark] Hint: Write your answer as x.xxx to y.yyy.  e.g. 0.123 to 1.234.

 

  1. Interpret your 95 % CI from the previous question, by filling in the gaps to the sentence below. [3 marks]

 

This interval <A> the value of <B>, so it <C> statistically significant

A: includes; excludes

B: 0; 1

C: is; is not

 

 

  1. Calculate the Z-statistic (2 decimal places)[1 mark]

 

  1. Calculate the p-value (3 decimal places)[1 mark]

 

  1. Interpret the p-value from the previous question [3 marks]

 

As the p-value is <A> than 0.05, the null hypothesis is <B>.

The odds of having a slow reaction time is <C> left and right handed people.

 

A:   greater than  ;  less than

B:   not rejected  ; rejected

C:   the same among ; different between

 

 

 

(Section F follows on the next page…)

 

Section F: Using statistical packages (12 marks) 

 

 

The Council of Roberton has contacted you and is really interested in the association between physical activity and how this impacts on your reaction time in the test.

Is there a correlation between the physical activity reported and their reaction times? You are going to need to justify your answer using appropriate graphs, interpreting correlation coefficients and appropriate summary conclusions.

 

  1. Draw a graph for the variables:physical activity and reaction time.

Please attach the graph as a file below.

In the text box, type the file name only.    [5 marks]

 

  1. What is your line of best fit? (All numbers to 4 decimal places)[1 mark]

 

  1. What is the predicted reaction time for someone with 3 hours of physical activity per week?  (3 decimal places)[1 mark]

 

  1. State your r (correlation) value (4 decimal places)[1 mark]

 

  1. State your R2(coefficient of determination) value (4 decimal places) [1 mark]

 

  1. Using your results from this section interpret your data by completing this sentence. [3 marks]

 

“Overall, there was a [X] correlation between reaction times and physical activity. [Y] in physical activity were correlated with [Z] reaction times of individuals.”

 

  • = strong negative;     weak negative;     weak positive;     strong positive
  • = increases ; decreases
  • = increased;   decreased

 

 

Section G: Putting it all together (10 marks) 

 

Congratulations! This is the end of your investigation.

 

Now it is time to finalise those conclusions and submit your recommendations to the Council.

 

  1. Describe your results and conclusions. Based on these, suggest recommendations in the form of a public health response that the Council of Roberton could implement to help improve this situation (max 300 words)    [10 marks]

 

Key points required:

  • Your results (numbers and interpretation)
    1. Gender (Section D)
    2. Handedness (Section E)
  • Physical activity (Section F)
  • A health promotion approach response and recommendation to the council
  • Your overall conclusion

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