HOW TO: Statistical Inference (New study design topic)

[evandowsett]

Hey guys, I recently held a poll in this forum to find out what people are struggling with most, and it seemed that a lot of people are having trouble with the new study design topic. I've decided to write a quick guide with some example questions for you below


Sample Statistics:
Example: In a recent survey, 1 in 5 students indicated that they ate potato crisps or other salty snacks at least four times per week. Is this a sample statistic or a population parameter?

Answer: This is a sample statistic. Why?
A sample statistic gives an estimated statistic based on a sample from a population. A population parameter gives a true statistic of a whole population.

Eg. With the above question, it is highly unlikely that the survey asked all students in Australia (or whatever the population is) if they eat potato crisps. Therefore, this estimated statistic is representative of the whole population as part of a sample, because the survey was conducted with a portion of the population


Distribution of p
Example:
   10. In a particular country town, the proportion of employment in the farming industry is 0.62. Five people aged 15 years and older are selected at random from the town.
   a. What are the possible values of the sample proportion, p^, of workers in the farming industry?
   b. Use this information to construct a probability distribution table to represent the sampling distribution of the sample proportion of workers in the farming industry.
   c. Find the probability that the proportion of workers in the farming industry in the sample is greater than 0.5.

Answer:

Confidence Intervals/Margin of Error
Example: Tatiana is conducting a survey to estimate the proportion of Year 12 students who will take a gap year after they complete their VCE. Previous surveys have shown the proportion to be approximately 15%. Determine the required size of the sample so that the margin of error for the survey is 3% in a confidence interval of approximately 95% for this proportion.

Answer:

Confidence interval: A confidence interval is the proportion of data that lies in the middle of the graph. This means that if you have a confidence interval of 95%, 95% of data is in the middle, which leaves 2.5% on each side. If you have a 99% confidence interval, this leaves 0.5% of data on each side.


How to work out z-score:

Margin of error: A margin of error is very difficult to define. It is explained in textbooks as “The distance between the endpoints of the confidence interval and the sample estimate”. It’s a bit ambiguous what this means, but you don’t really need to understand it. All you need to know is this:

where M = margin of error
z = z-score of confidence interval (use above working to figure this out)
p = sample proportion
n = sample size

Good luck guys and I hope this helps! Let me know if you have any questions

[MightyBeh]

Thank you for the excellent guide Evan, I've added it to the Methods Resource Thread.

On changing the size of images, when using an [ img] tag, you can include parameters like width=x and height=y to change how it's displayed in pixel measurements. This doesn't actually lower the resolution of the picture and it can be enlarged for viewing by clicking on it in the post. For example:

Code: [Select]

[img width=1000 height=1000]http://imageurl.com/image.png[/img]
Generally numbers between 500-1000 for width work well.

[heids]

Beautiful!  Thanks a heap, Evan

[qwertyu1234567]

Thanks so much, this is great   

[evandowsett]

Thank you for the excellent guide Evan, I've added it to the Methods Resource Thread.

On changing the size of images, when using an [ img] tag, you can include parameters like width=x and height=y to change how it's displayed in pixel measurements. This doesn't actually lower the resolution of the picture and it can be enlarged for viewing by clicking on it in the post. For example:

Code: [Select]

[img width=1000 height=1000]http://imageurl.com/image.png[/img]
Generally numbers between 500-1000 for width work well.

Hey MightyBeh, thank you for adding it to the Resources thread! I'm glad it's helped some people out and hope everyone can take some value from it over the next few days before the exams. Thanks for the image tip, you learn something new every day!

heidiii and qwerty, you're very welcome

Guys, again, let me know if you have any questions and I'm more than happy to answer them. Even post up a pic of a question that you'd like a hand with if you want 

[qwertyu1234567]

Guys, again, let me know if you have any questions and I'm more than happy to answer them. Even post up a pic of a question that you'd like a hand with if you want 

Hi evandowsett,

Would you be able to provide me with a quick run through of probability?
The different types, how to identify what type of probability the question is referring to and how to use the different types.
Thank you so much I just can't seem to get my head around it all!

[evandowsett]

Hi evandowsett,

Would you be able to provide me with a quick run through of probability?
The different types, how to identify what type of probability the question is referring to and how to use the different types.
Thank you so much I just can't seem to get my head around it all!

Hey qwerty, I've created a custom guide just for you! Find it here - HOW TO: Probability Guide (When and how to use each type of probability)

I hope it helps, let me know if you have any questions in that thread

[Jesse_ando]

Hi Evan! thanks heaps for the examples, just one question about the Confidence Intervals/Margin of Error
The 3rd page gave the value 544 for N, but for n being people, don't you have to round up to a whole number always? the answer I got was 544.227, so the next whole number would be 545?

[evandowsett]

Hi Evan! thanks heaps for the examples, just one question about the Confidence Intervals/Margin of Error
The 3rd page gave the value 544 for N, but for n being people, don't you have to round up to a whole number always? the answer I got was 544.227, so the next whole number would be 545?

Hey Jesse, that's a good question - it depends on how the question is worded and what the context of the question is. In this question, it asks for the 'required size of the sample' which to me means just a rounded number to the nearest whole number. If the question was worded in a way that asked 'what is the minimum sample size to make a margin of error of at least 3%' then it would need to be 545, however because it doesn't ask for it in that way we can simply round down. The answer in the back of the book is officially 544, and this is my reasoning behind that answer hopefully that makes sense. It's a bit hard to work out when to round down and when to round up, but it all depends on the way the question is worded.

[Jesse_ando]

Hey Jesse, that's a good question - it depends on how the question is worded and what the context of the question is. In this question, it asks for the 'required size of the sample' which to me means just a rounded number to the nearest whole number. If the question was worded in a way that asked 'what is the minimum sample size to make a margin of error of at least 3%' then it would need to be 545, however because it doesn't ask for it in that way we can simply round down. The answer in the back of the book is officially 544, and this is my reasoning behind that answer hopefully that makes sense. It's a bit hard to work out when to round down and when to round up, but it all depends on the way the question is worded.

Yep ok, that makes sense. So unless specifically asked for minimum/ maximum sample size (where you round up), you just round to whatever is closest?

[evandowsett]

Yep ok, that makes sense. So unless specifically asked for minimum/ maximum sample size (where you round up), you just round to whatever is closest?

Yeah exactly Jesse!

[lastminute]

Helllo!!
Thanks for the awesome post, I just have a lil q, could you explain normal approximation? My teacher said its not on the study design but it is mentioned in trial exams and the textbook. All I know about it is the conditions for it to be normal approx and to use E(x) = np VAR(x) = np(1-p) but is that all there is to it?
Thank you!

[clockerrs11]

Thanks for this guide!

But can you possibly go through any non-tech statistical interference questions? I'm quite worried and don't know what to expect when it comes to statistical interference in the non-tech exam.

[MB_]

Thanks for this guide!

But can you possibly go through any non-tech statistical interference questions? I'm quite worried and don't know what to expect when it comes to statistical interference in the non-tech exam.

Have you had a look at the sample exam? There is a statistical inference question on there

Sample exam: http://www.vcaa.vic.edu.au/Documents/exams/mathematics/mathmethods-specs-sample-w.pdf

[clockerrs11]

I've done that, is that all we are expected to know about statistical interference without a calculator?