Download presentation

Presentation is loading. Please wait.

Published byMaliyah Crouse Modified over 2 years ago

1
The Right Questions about Statistics: How confidence intervals work Maths Learning Centre The University of Adelaide A confidence interval is designed to give a RANGE of possible answers for a “WHAT’S THE NUMBER?” question, using DATA from a sample. You calculate which numbers could have been likely to produce your data.

2
What is the median number of chapters in a novel? Randomly choose 12 books Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

3
Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20 Which possible medians might be likely to produce this data? For each particular median, we could do a hypothesis test to answer the question (in this case it’s called the sign test) … 1214162018101113151719212223

4
1214162018101113151719212223 ? SIGN TEST P-value = 0.0005 Under 0.05, so NO, the median is not 10. Is the median for all books 10? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

5
1214162018101113151719212223 ? SIGN TEST P-value = 0.0005 Under 0.05, so NO, the median is not 11. Is the median for all books 11? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

6
1214162018101113151719212223 ? SIGN TEST P-value = 0.0005 Under 0.05, so NO, the median is not 12. Is the median for all books 12? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

7
1214162018101113151719212223 ? SIGN TEST P-value = 0.001 Under 0.05, so NO, the median is not 13. Is the median for all books 13? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

8
1214162018101113151719212223 ? SIGN TEST P-value = 0.02 Under 0.05, so NO, the median is not 14. Is the median for all books 14? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

9
1214162018101113151719212223 ? SIGN TEST P-value = 0.23 Over 0.05, so YES, the median could be 15. Is the median for all books 15? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

10
1214162018101113151719212223 ? SIGN TEST P-value = 0.75 Over 0.05, so YES, the median could be 16. Is the median for all books 16? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

11
1214162018101113151719212223 ? SIGN TEST P-value = 1.0 Over 0.05, so YES, the median could be 17. Is the median for all books 17? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

12
1214162018101113151719212223 ? SIGN TEST P-value = 0.56 Over 0.05, so YES, the median could be 18. Is the median for all books 18? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

13
1214162018101113151719212223 ? SIGN TEST P-value = 0.11 Over 0.05, so YES, the median could be 19. Is the median for all books 19? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

14
1214162018101113151719212223 ? SIGN TEST P-value = 0.01 Under 0.05, so NO, the median is not 20. Is the median for all books 20? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

15
1214162018101113151719212223 ? SIGN TEST P-value = 0.001 Under 0.05, so NO, the median is not 21. Is the median for all books 21? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

16
1214162018101113151719212223 ? SIGN TEST P-value = 0.0005 Under 0.05, so NO, the median is not 22. Is the median for all books 22? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

17
1214162018101113151719212223 ? SIGN TEST P-value = 0.0005 Under 0.05, so NO, the median is not 23. Is the median for all books 23? Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20

18
1214162018101113151719212223 That is, all the medians that would give a p-value of over 0.05. “95% confidence interval” It shows all the medians that could be true based on hypothesis tests at the 5% level of significance. Book# Chapters 1 21 2 16 3 14 4 18 5 14 6 16 7 19 8 15 9 17 10 13 11 19 12 20 This is the (95%) confidence interval You could say it’s the medians I am “happy to believe” based on my data.

19
BookWeight (g) 1 242 2 366 3 424 4 312 5 307 6 238 7 317 8 265 9 317 10 314 11 217 12 379 What is the mean weight in a novel? Randomly choose 12 books Another example...

20
BookWeight (g) 1 242 2 366 3 424 4 312 5 307 6 238 7 317 8 265 9 317 10 314 11 217 12 379 Which possible means might be likely to produce this data? For each particular mean, we could do a hypothesis test to answer the question (in this case it’s called the t-test) … Another example... 250300350200400

21
250300350200400 BookWeight (g) 1 242 2 366 3 424 4 312 5 307 6 238 7 317 8 265 9 317 10 314 11 217 12 379 ? T-TEST P-value = 0.00007 Under 0.05, so NO, the mean is not 200. Is the mean for all books 200?

22
250300350200400 BookWeight (g) 1 242 2 366 3 424 4 312 5 307 6 238 7 317 8 265 9 317 10 314 11 217 12 379 ? T-TEST P-value = 0.00008 Under 0.05, so NO, the mean is not 201. Is the mean for all books 201?

23
250300350200400 BookWeight (g) 1 242 2 366 3 424 4 312 5 307 6 238 7 317 8 265 9 317 10 314 11 217 12 379 ? T-TEST P-value = 0.00009 Under 0.05, so NO, the mean is not 202. Is the mean for all books 202?

24
250300350200400 BookWeight (g) 1 242 2 366 3 424 4 312 5 307 6 238 7 317 8 265 9 317 10 314 11 217 12 379 And so on...

25
250300350200400 BookWeight (g) 1 242 2 366 3 424 4 312 5 307 6 238 7 317 8 265 9 317 10 314 11 217 12 379 “95% confidence interval” That is, all the means that would give a p-value of over 0.05. It shows all the means that could be true based on hypothesis tests at the 5% level of significance. This is the (95%) confidence interval You could say it’s the means I am “happy to believe” based on my data.

26
250300350200400 BookWeight (g) 1 242 2 366 3 424 4 312 5 307 6 238 7 317 8 265 9 317 10 314 11 217 12 379 “95% confidence interval” These ends would have given exactly 0.05 in the hypothesis test. BUT you don’t have to go through all this to find a confidence interval! You just have to figure out where the ends are. So you find them by doing the hypothesis test calculation backwards...

27
CI ends = mean ± t* × std. Error = 269 & 347 t = mean – 300 std. Error = 0.46 t* = ± 2.20 More than 0.05, so the mean could be 300. p = 0.65 HYPOTHESIS TEST Assume mean is 300 Use assumed mean and data to calculate a test statistic Use test statistic to get p-value. CONFIDENCE INTERVAL Assume P-value is 0.05 Use p-value to get “critical” test statistics. Use critical values to get two means. Compare p-value to 0.05 to decide. 95% confidence interval is between these. -2.00.01.02.0 95% CI is from 269 to 347 250300350200400

28
BookWeight (g) 1 242 2 366 3 424 4 312 5 307 6 238 7 317 8 265 9 317 10 314 11 217 12 379 Let’s go over that again… What is the mean weight in a novel? Randomly choose 12 books Choose a hypothesis test, and a significance level. T-Test, 0.05 Use critical values and your data to calculate the two ends. CI ends = mean ± t* × std. Error = 269 & 347 State the answer. The 95% CI is from 269g to 347g. Find the critical values of the test statistic. t* = ± 2.20 -2.00.01.02.0

29
So this is how to find a confidence interval: Have a “what’s the number?” question. Collect data. Choose a matching hypothesis test. Work backwards to calculate two ends. The confidence interval is between these two values.

30
And this is what a confidence interval means: The values in the CI would be retained with a matching hypothesis test. The values in the CI are those you are “happy to believe” based on your data. The values in the CI have a high chance of producing data like yours.

Similar presentations

OK

MULTIPLYING MONOMIALS TIMES POLYNOMIALS (DISTRIBUTIVE PROPERTY)

MULTIPLYING MONOMIALS TIMES POLYNOMIALS (DISTRIBUTIVE PROPERTY)

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on dos operating system Ppt on world book day ideas Ppt on genders for grade 1 Ppt on series and parallel circuits pdf Ppt on eia report bakken Ppt on self development articles Ppt on modern periodic table Ppt on ascending and descending order of numbers Electronics ieee papers ppt on sustainable buildings Ppt on cross docking definition