the one-sample t-test and the binomial test
So far we have learnt about two tests – the one-sample t-test and the binomial test. Both of these tests allow data to be collected from a sample in order to estimate a particular parameter (mean or proportion) in the population from which the sample was drawn. These tests allow this estimated mean or proportion to be compared to a mean or proportion that is already known for a particular population. For example, say we know the average height of SOL students in 2013 and we want to compare their average height to SOL students in 2014. We take a sample of SOL students in 2014 and measure their average height to estimate the height of all 2014 SOL students. We then compare this estimate to the known average height of SOL students in 2013. Note that as height is a metric variable, we would use the one-sample t-test to do this. If we were comparing proportions for categorical variables we would use the binomial test instead.
There are some further online exercises to help you master this week’s content in Week 3 of the Interactive Room.
Activity 1: Which statistical test?
Purpose: This activity will help you get more comfortable with statistics tests. This is a key skill that you will be tested on in the online test and the final exam and that you will need to pass this unit.
See the Discussion Board for more information.
Activity 2: Recognising dependent variables
Match the following dependent variables to the research hypothesis
Age
Computer ownership
Whether the proportion of people that own a computer in 2013 has changed since 2012 (categorical)
Lifespan
Attitude to tennis
Whether the proportion of people in Melbourne that say they enjoy playing tennis increases when the Australian Open is on (categorical)
Income
Deciding if the rats in Australia have a longer lifespan on average than those in Britain (metric)
Finding out how the age of people in our group compares to the rest of SOL students (metric)
Whether the average income of people in 2012 in Brisbane has changed since 2005 (metric)
Activity 3: Interpreting data and report writing
Purpose: To give you some early practice at exam style questions and report writing.
Purpose: In the Assessment task and the final exam, you are likely to be required to write a report for a binomial test. This question steps you through that process and will help make sure you are on track. Have a go at answering the questions in the activity on your group’s Discussion Board. Before doing so, read the following and then hover over each sentence in the report below for information about the need for that sentence.
Note that, as per usual, the report makes a prediction about the population, describes what was done with the sample, and then makes an inference and conclusion about the population. The report follows a typical format as follows:
• Hypothesis
• Description of sample and sample statistics
• Test used and results of test
• Confidence interval
• Conclusion
________________________________________
Report writing
In order to help you get started with report-writing for binomial tests, hover over each sentence in the report below to view helpful comments about it.
A study was conducted to determine whether the proportion of students that are married has changed since the seventies.
In a sample of 270 students, 21% were married. This is lower than in 1978 when 28% were married, and a Binomial test shows that the difference is significant n=270, p=.049. The 95% confidence interval indicates that between 16% and 26% of students are married in 2014.
As expected, the proportion of students who are married has changed in 2014 compared to the seventies.
See the Discussion Board for more information.
DISCUSSION BOARD INFORMATION
Objectives
Alan Healey Teaching Assistant Manager
Objectives for this week
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Howdy all,
This is a biggest week for content so far. I’ll break it down into the key components:
Objectives:
• To describe the distributions for metric and categorical variables
• To be able to choose and report the correct summary statistic
• To be able to run binomial and one-sample t-tests
Tasks:
• Read the Week 3 learning materials (Module 2: Reporting information about a single variable)
• Read pages 33-55 of the textbook
• Complete textbook exercises 2.1-2.21 (you’ll need to have SPSS for this)
• There are 3 activities to complete this week: 2 on the discussion board, and one in the Learning Materials section.
Assessment:
• Complete Topic Test 3 (there is a trial Topic Test to complete first)
There is an Excel spreadsheet in the Data Files and Calculator section that has the 95% confidence interval for proportions calculator (SPSS doesn’t do this).
If you feel like taking a break from learning for 20 minutes or so, I present to you one of my favourite TED talks and ultimately where my interest in statistics lies: Visualizing Data.
As with always, there are no silly questions, so if you’re not understanding something, let me know.
Al
ACTIVITY 1
Activity 1: Which statistical test?
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Purpose: This activity will help you get more comfortable with statistics tests. This is a key skill that you will be tested on in the online test and the final exam and that you will need to pass this unit
Your task: Determine which test would you need to use for each of these situations. Follow these steps and post answers for a, b and c
a. What is the variable being measured?
b. Is this variable metric or categorical?
c. Would you use a one-sample t-test or a binomial test?
1. Finding out how the age of people in our group compares to the rest of SOL students
2. Whether the proportion of people that own a computer in 2013 has changed since 2012
3. Deciding if the rats in Australia have a longer lifespan on average that those in Britain
4. Whether there are more people that live in your street that walk to work than those that live in the rest of your suburb
5. Whether the proportion of people in Melbourne that say they enjoy playing tennis increases when the Australian Open is on
6. Whether the average income of people in 2012 in Brisbane has changed since 2005
ACTIVITY 3
Activity 3: Interpreting data and report writing
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Purpose: To give you some early practice at exam style questions and report writing
Time/Length: 30 mins and complete by Sunday of Week 3.
Your task: Interpret the SPSS output below to answer the following questions about this research scenario.
A teacher asked her students to complete a science project and asked all students to rate their project as either a failure or success. The teacher runs a binomial test on a sample of her students this year, comparing it to the result from her class last year
I will upload the diagram
a. How many students were in the sample?
b. What proportion of the class thought their project was a success?
c. Which proportion of the class last year thought their project was a success?
d. Is this result significantly different? How do you know this?
e. Write a short report following the formal statistics structure (refer to example report on page 52 in etextbook. Tip: Use the 95% confidence interval calculator in the Week 3 Learning Materials or the Data Files and Calculator link to get the population bounds for the proportion. It’s fine to use either the excel version or the Java applet.
Group 1 = success (shown here as category 1.00), Group 2 = failure
READINGS
Java. (n.d.). Retrieved from http://java.com/en/
foundationsofstats. (2012). STA102_Week3_Part1_One sample t test [Video file]. Retrieved from http://www.youtube.com/watch?v=kTjmMfjXmOw
foundationsofstats. (2012). STA102 Week3_Part 2_Binomial test [Video file]. Retrieved from http://www.youtube.com/watch?v=hienyigh5IE
Statcats. (n.d.). Statcats home. Retrieved from http://statscats.weebly.com/
Images
Statcats. (n.d.). Statcats logo [image]. Retrieved from http://statscats.weebly.com/