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EAB > Estimation and Confidence Intervals > Flashcards

Estimation and Confidence Intervals Flashcards

1
Q

Why are samples taken?

A
  • impractical/impossible to study whole pop so if select one sample from a pop + calc the mean value, then sample mean will provide some info about overall mean in pop.
  • Sample data used to draw conclusions about pops
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2
Q

What is the disadv of sampling?

A
  • Sample data are imprecise – diff samples give diff estimates (known as sampling error)
  • data collected from sample will never provide full info about whole pop
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3
Q

How is uncertainty about not having all of the data dealt with?

A

Statistical methods based on probability theory are used to quantify this uncertainty

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4
Q

What is the sample mean?

A

estimation of pop parameter e.g. av height in UK

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5
Q

What is the statistical estimation?

A

estimate pop parameter from sample/observed statistic

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6
Q

Why is estimation never perfect?

A

sample only selection from pop - diff samples give diff results

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7
Q

What is sampling distribution of the mean?

A

sample estimates (means) calc from multiple samples from same pop will have dis of differing values

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8
Q

How are sampling distributions of the mean interpreted?

A

values of sample means close to the overall population mean are more likely (more common) than extreme values.

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9
Q

What are the 2 important relationships of sample size and SD to true mean?

A
  • bigger sample size - estimate closer to true mean (more precise)
  • smaller SD (spread of data - “
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10
Q

What is standard error?

A

The SD of the sample means (i.e. sampling distribution of mean)

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11
Q

How is SE calc?

A

SD / square root of pop size (n)

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12
Q

How does changing SD or N affect SE

A
  • Smaller SD/larger N dec SE (precision) - more precise estimate
  • Larger SD/smaller N inc SE (precision) - less precise estimate
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13
Q

Why are confidence intervals used?

A
  • as can’t deduce exact pop value from sample, can use sample to obtain CI
  • ind precision/unprecision of sample values as estimates of pop values
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14
Q

How can the Normal distribution be used?

A
  • can use to calc a range of possible values for the true population mean (confidence intervals for means and other estimates)
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15
Q

What is formula for calc 95% confidence interval for a mean from a large sample?

A
  • mean - 1.96 x SE to mean + 1.96 x SE
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16
Q

How can 95% CI be interpreted?

A
  • True pop mean expected to lie in the range of sample mean +/- 1.96 SE in 95% of all calc
  • say that ‘we have 95% confidence that the true value/mean in the pop from which the sample was taken lies within these 2 values
17
Q

What are the assumptions in calc 95% CI?

A
  • Normal data/large sample (at least 60)
  • Sample chosen at random from pop
  • Obsv indep of each other (can’t take same obsv twice)
18
Q

How is SE of a prop calc?

A
  • a certain prop in pop has a condition.
  • (n) individuals altogether and (r) with the condition then estimate the population prop by p = r/n.
  • SE = square root of p (pop prop with characteristic) x 1-p (pop prop without characteristic) / n (sample size)
19
Q

What are the assumptions for calc 95% CI for prop?

A
  • Sample chosen at random from pop
  • Obsv indep of each other
  • Prop with characteristic not close to 1/0
  • n x p + n x (1-p) greater than 5 (basically large sample)
20
Q

What happens if np + n(1-p) greater than 5?

A

p normally dis assuming that the sample is large + expected mean equal to p.

21
Q

How is a prop taken from a large sample?

A
  • take sample of indiv from pop of interest + each one has/doesn’t have specific characteristic
22
Q

What is formula for calc 95% CI for prop of large sample?

A

p - 1.96 x SE to p + 1.96 x SE

23
Q

How do you interpret 95% confidence interval for a proportion?

A
  • a range of values which has 95% probability of containing the true population proportion
  • say ‘we have 95% confidence that the true value of the proportion in the population from which the sample was taken, lies within the interval’
24
Q

What is defined as a large sample for a sample mean and how does this affect CI?

A
  • sample size of 100 is large so sample mean follow an approx normal distribution irrespective of underlying distribution of data so multiplier 1.96 can be used to calc confidence intervals.
25
Q

What is defined as a large sample for a sample prop and how does this affect CI?

A
  • the sample size can be considered large if r and n-r are both greater than five.
  • If this does not hold, an exact Binomial confidence interval can be calculated.
26
Q

How do you build up ev from sample to pop?

A
  • have pop + need to identify specific parameter e.g. mean no. of cigs smoked per day by men
  • use study design e.g. cross-sectional sample survey
  • get sample estimate from this pop e.g. sample mean no. of cigs smoked per day by men
  • deduce from sample to infer about pop
27
Q

If estimating some quantity from data, how can quantify imprecision in estimate?

A

using a confidence interval

28
Q

If testing a hypothesis, how can quantify imprecision in estimate?

A

can do a statistical significance test which helps to weigh evidence that the sample diff observed is a real diff

29
Q

Why is SE sig?

A
  • summarises 2 relationships of sample size + SD
  • gives ind of extent of sampling error (how much sample tends to vary from pop/true mean)
  • provides estimate of precision of the sample mean
30
Q

What are CI?

A
  • range within which pop value likely to be

- e.g. 95% CI is a margin of error around the estimate which indicates how precise it is

31
Q

What is dis of large samples + sig?

A
  • the sample means will follow a Normal distribution bc of mathematical theorem (central limit theorem)
  • Using this, can calc SE of a prop + then estimate 95% confidence interval for a sample prop.
32
Q

What about samples smaller than 100?

A

data needs to follow Normal distribution + t distribution used to calc CI

EAB (5 decks)

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