Revision - PowerPoint PPT Presentation

About This Presentation
Title:

Revision

Description:

... hypothesis that the size of cuckoo's eggs differ depending on the ... There is evidence that the size of cuckoo egg differs depending of the type of nest. ... – PowerPoint PPT presentation

Number of Views:42
Avg rating:3.0/5.0
Slides: 32
Provided by: computings48
Category:
Tags: cuckoo | revision

less

Transcript and Presenter's Notes

Title: Revision


1
Revision
  • Ideas of hypothesis testing
  • One-sample t-test
  • Two independent samples t-test
  • Paired t-test

2
Stages in statistical analysis
3
Example 1
  • Established records show that the lengths of
    mussels from an estuary are normally distributed
    with a mean of 30 mm. A random sample of 25
    mussels was taken from a polluted beach.
  • Is there sufficient evidence to conclude that
    pollution appears to inhibit the growth of
    mussels?

4
Data
  • 26.72 16.44 18.72 41.39 21.31
  • 29.87 19.06 17.03 15.29 23.95
  • 18.15 31.22 26.33 34.88 17.57
  • 21.02 26.45 25.56 21.32 30.40
  • 19.12 42.56 39.63 35.12 25.95

5
Display the data
6
One-sample t-test
  • Null hypothesis pollution has no effect.
  • Mean length has not changed.
  • H0 ? 30
  • Alternative hypothesis pollution inhibits growth
  • Mean length is less than previously
  • H1 ? lt 30
  • P-value What is the probability of obtaining a
    mean of 25.76 or less if the true mean is 30?

7
Analysegt Compare means gt One-sample t
8
Output
9
Conclusion
  • Always state the final conclusion in terms of the
    original problem and avoiding statistical jargon.
  • There is evidence to suggest that pollution does
    inhibit the growth of the mussels.
  • The mussels from the polluted area are 4.24cm
    smaller on average.
  • 95 confidence interval for mean length of
    polluted mussels is (22.42, 29.11)

10
Assumptions
  • Test assumes that the data are from a normal
    distribution.
  • Check using a Q-Q or normal plot.

11
Example 2
  • Data were collected to test the hypothesis that
    the size of cuckoos eggs differ depending on the
    type of nest in which they lay their egg.
  • Samples of cuckoos eggs from the nests of hedge
    sparrows and reed warblers were obtained.

12
Choice of test
  • The two sets of data are independent of each
    other so the appropriate test to examine the
    difference in the means of the two types of eggs
    would be a independent or two-sample t-test
  • Assuming both sets of data come from normal
    distributions.

13
Boxplots
14
Hypotheses
  • H0 ?1 - ?2 0
  • H1 ?1 - ?2 ? 0
  • using a two-tailed alternative

15
Analysegt Compare means gt Independent- samples t
test
16
Summary statistics
17
Results of hypothesis test
Note equal variances should not be assumed
18
Conclusion
  • Always state the final conclusion in terms of the
    original problem and avoiding statistical jargon.
  • There is evidence that the size of cuckoo egg
    differs depending of the type of nest. The eggs
    in hedge sparrow nests are larger that those in
    reed warbler nests.
  • How much larger?

19
Confidence interval for the difference in two
means
Suggests eggs in hedge sparrows nests are between
0.45 and 1.53 mm longer, on average, than those
in reed warblers nests.
20
Assumptions
  • Test assumes that the data are from a normal
    distribution.
  • Check using a Q-Q or normal plot for each group.
  • Use test assuming equal variance, if possible.
  • Not possible for this example.

21
Example 3
  • Does smoking increase the aggregation of
    platelets in the blood?
  • Aggregation measured in 14 individuals before and
    after smoking a cigarette

22
Data
23
Choice of test
  • Two results obtained from each individual.
  • Data for before and after are clearly not
    independent.
  • Paired t-test is appropriate.

24
Hypotheses
  • H0 ?d 0
  • H1 ?d gt 0
  • using a one-tailed test

25
Display the data
26
Analysegt Compare means gt Paired samples t test
27
Results
28
Null hypothesis
  • Often the aim of an experiment is to look for a
    difference or an improvement.
  • Null hypothesis is always that there is no
    difference.
  • A significant result means that this hypothesis
    of no difference is rejected.
  • If a result is not significant then the null
    hypothesis is not rejected.

29
Hypothesis test
  • Do the sample means differ from the hypothesised
    mean by
  • A small amount that can be explained by sampling
    error
  • A large amount indicating the null hypothesis of
    no difference is wrong

30
P-value (sig)
  • Degree of difference measured by the p-value, the
    probability of obtaining the sample mean if the
    hypothesised mean is correct.
  • Small difference, large p-value
  • Large difference, small p-value

31
Confidence interval
  • Given inherent error due to the sampling process,
    what range of values seem feasible for the mean
    of the population?
  • Can be used for
  • Estimating the mean with no hypothesis test
  • Checking a hypothesised value
  • Estimating the mean when the null hypothesis has
    been rejected
Write a Comment
User Comments (0)
About PowerShow.com