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Inference. Using PPDAC for comparison situations at Level 8. To Do!. L ink informed contextual knowledge to a conclusion Compare findings with research findings Make a call and say why and what it means- informed by research Think of further questions that may further the investigation

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inference

Inference

Using PPDAC for comparison situations at Level 8

to do
To Do!
  • Link informed contextual knowledge to a conclusion
  • Compare findings with research findings
  • Make a call and say why and what it means- informed by research
  • Think of further questions that may further the investigation
  • Demonstrate insight
  • Understand variability
  • Discuss the affect an outlier might make
slide3

Achieved- doing it

  • Merit – justifying it, refer to population
  • Excellence – Insight, research
excellence thoughts
Excellence thoughts
  • Reasons for the results
  • Comparing more than one set
  • Reflecting on the process used to make the formal inference
  • Discussing sampling variability
comparison questions must clearly include
Comparison questions must clearly include:
  • Variable that is being examined (height in cm)
  • Groups that are being compared (Year 11 boys and Year 11 girls)
  • Population that inferences are being made about (New Zealand Year 11 boys and New Zealand Year 11 girls)
  • Variable being examined
  • Statistic (DIFFERENCE in sample median heights between boys and girls)
example
Example

The purpose of this investigation is to determine if the median Red Blood Cell counts (RCC) for male Australian athletes ishigher than the median RCC for female Australian athletes from this sample of 202 Australian athletes from the Australian Institute of Sport.

  • The difference in sample median RCC levels between male and female athletes from this
  • sample will be used to make a formal inference about RCC levels of male and female athletes in Australia.
variable being examined
Variable being examined

The purpose of this investigation is to determine if the median Red Blood Cell counts (RCC) for male Australian athletes ishigher than the median RCC for female Australian athletes from this sample of 202 Australian athletes from the Australian Institute of Sport.

  • The difference in sample median RCC levels between male and female athletes from this
  • sample will be used to make a formal inference about RCC levels of male and female athletes in Australia.
comparative word
Comparative word

The purpose of this investigation is to determine if the median Red Blood Cell counts (RCC) for male Australian athletes ishigher than the median RCC for female Australian athletes from this sample of 202 Australian athletes from the Australian Institute of Sport.

  • The difference in sample median RCC levels between male and female athletes from this
  • sample will be used to make a formal inference about RCC levels of male and female athletes in Australia.
sample statistic
Sample Statistic

The purpose of this investigation is to determine if the median Red Blood Cell counts (RCC) for male Australian athletes ishigher than the median RCC for female Australian athletes from this sample of 202 Australian athletes from the Australian Institute of Sport.

  • The difference in sample median RCC levelsbetween male and female athletes from this
  • sample will be used to make a formal inference about RCC levels of male and female athletes in Australia.
population
Population

The purpose of this investigation is to determine if the median Red Blood Cell counts (RCC) for male Australian athletes ishigher than the median RCC for female Australian athletes from this sample of 202 Australian athletes from the Australian Institute of Sport.

  • The difference in sample median RCC levels between male and female athletes from this
  • sample will be used to make a formal inference about RCC levels of male and female athletes in Australia.
slide16

The purpose of this investigation is to determine if the median systolic blood pressure mmHg (SBP) of male participants is higher than the median SBP of female participants from this sample of 200 participants from this study.

  • The difference between the median SBP of the male and female participants will be used to make a formal inference about the SBP of British male and females with high fat diets.
slide17
Plan
  • The sampling method used is not simple random samplingas the participants were selected by their doctors to participate in the study. There is the possibility of self-selectionwhere participants could choose not to participate in the study which could cause biasin the sample and thus affect the inference about the population.
  • The sampling size of the study is small (n=200) which could cause possible inferences about the population to not be accurate. There was no information provided where in the UK the sample was taken. Samples from an urban population could be considerably higher because of a more sedentary lifestyle as compared to a rural population.
shift centres median and middle 50
Shift/ Centres – Median and Middle 50%
  • The median of the sample male SBP is 105.9 mmHg.
slide21

The median of the female SBP from the sample is 104.8 mmHg.The median male SBP from this sample has shifted further upthe scale when compared to the females SBP. There is not much shift which could mean that back in the population, there is not muchdifference between the SBP of either males or females.

slide22

The middle 50% of the male SBP has shifted slightly further upthe scale than the female’s middle 50% SBP. There is not much shift in the sample male’s middle 50% comparison to the sample female’s middle 50% SBP which could mean there is not much difference between the population middle 50% between the genders.

spread iqr overlap
Spread (IQR)/Overlap
  • The Inter-Quartile Range (IQR) for the sample male SBP is (UQ – LQ = IQR:
  • 110.3 – 102.6 = 7.7).
  • The Inter-Quartile Range (IQR) for the sample female SBP is (UQ – LQ = IQR:
  • 109.7 – 101.0 = 8.7).
slide24

The IQR for the sample male SBP is smallerin comparison to the sample female SBP. This could mean that in the population there could be less variability for the male SBP as compared to the female SBP.

slide25

There is muchoverlapof the IQRs between the sample male SBP and sample female SBP. This could mean that in the population there is not much difference between the SBP of males and females as the two samples are very similar.

shape symmetry skew and tails
Shape – Symmetry, Skew and Tails
  • By looking at the dot plots, the sample male and female SBP plots are symmetrical. This is reflected in the box and whisker plots as there is symmetry in the middle 50% of both samples. This could mean that in the population there is a symmetrical distribution of both males and females SBP. This could be a reflection of the large sample taken (n=200) which could give a broad spectrum of participants thus giving the range of SBPs.
unusual features
Unusual Features
  • There are no outstanding unusual features such as extreme outliers in either samples of male and female SBP. There are two modes in the sample female SBP at approximately SBP = 101 and 105mmHg.This could be a result of the measuring implements used but are not unusual as they are within the middle 50% of the data.
conclusion
Conclusion
  • The sample median male SBP is between-0.50 mmHg and 3.30 mmHghigher than the sample female median SBP. The call cannotbe made that back in the population of British male and females consuming a high fat diet there is a difference between male and female SBP.
  • The formal inference used was a bootstrap confidence interval (-0.50 mmHg, 3.30mmHg) of the sample differences between the male and female SBP. The call cannot be made that back in the population of British male and females consuming a high fat diet there is a difference between British male and female SBP.
a key idea underpinning the construction of a bootstrap confidence interval
A key idea underpinning the construction of a bootstrap confidence interval
  • With a point estimate (e.g., a sample mean), the uncertainty about the true value of the parameter (the population mean) is due to the fact that the sample mean varies from sample to sample about the true mean. The width of a confidence interval has to be large enough to take the extent of this sample-to-sample variation of the sample mean into account.
a key idea underpinning the construction of a bootstrap confidence interval1
A key idea underpinning the construction of a bootstrap confidence interval
  • A key idea underpinning the construction of a bootstrap confidence interval is that the extent of this sample-to-sample variation in the sample means is very similar to the extent of the sample-to-sample variation in the re-sample means. So the distribution of the re-sample mean (the bootstrap distribution) is used to estimate the extent of the variation in the sample mean and this allows us to use the bootstrap distribution to determine the limits of the bootstrap confidence interval.
slide32

Our confidence in a particular bootstrap confidence interval comes from the fact that this method produces an interval which contains the true value of the parameter a very high percentage of the time.

slide33

A bootstrap confidence interval for a parameter can be thought of as a range of believable values for the true parameter value.