Estimation and Confidence Intervals Flashcards

1
Q

Definition of statistical estimation

A

Estimate the parameter being investigated by finding the mean value from a random sample

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2
Q

Definition of sample/point estimation

A

Use of sample data to calculate an estimate of an unknown parameter

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3
Q

Definition of confidence interval

A

A range of plausible values for an unknown calue

Can quantify uncertainty and imprecision

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4
Q

Definition of sampling error

A

Different samples give different estimates

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5
Q

Definition of sample distribution

A

Sample estimates calculated from multiple ampler from the same population will have varying distribution values

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6
Q

Definition of standard error

A

Indication of the extent of the sampling error
Tells us how much a sample mean tends to cary from the population mean
Provides and estimate of the precision of the sample mean

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7
Q

How would you estimate a value from a large population

A

Impossible to measure everyone in a population

  1. Take a random sample, find the sample mean
  2. Different samples => different point estimates
  3. Sample estimates vary around a true value
  4. Can use this data to work out a confidence interval
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8
Q

What is the confidence interval and what is it used for

What can it not tell you

A

Cannot deduce exact population value from a sample
Can use sample to obtain a confidence interval
-Range within which a population value is likely to be

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9
Q

Describe the pathway in an investigation and show how you’d use the info found on the population parameter

A

Design a study based on the population parameter
Take a sample and estimate the parameter
Take the results and deduce that it applies to the whole population

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10
Q

What is sampling error

How does it arise

A

Different samples => different estimates

Provide an incomplete picture of the population

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11
Q

What 2 values help you find the true mean

A

Bigger sample size => estimate closer to true mean

Smaller SD => estimate closer to true mean

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12
Q

What is the standard error

What is the equation for standard error

A

Tells you how much a sample mean tends to vary from the true population
Estimate of precision of sample mean

SE = SD/√N

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13
Q

How do you increase precision if you can change the SD or the sample size

A

Decreased SD or increased sample size => smaller SE => increased precision

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14
Q

What does it mean to have a 95% confidence interval

A

True mean expected to lie within range in 95% of calculations

Lower confidence limit = -1.96 SD of sample mean
Upper confidence limit = +1.96 SD of sample mean

Confidence interval = range between lower confidence limit and upper confidence limit

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15
Q

What are the 3 assumptions in calculating the confidence interval

A

Normal data or large sample ≥60)
Sample chosen at random from population
Observations are independent of each other

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16
Q

How do you calculate the lower confidence and upper confidence limit

How do you use these values to find the confidence interval for the mean

A

SE = SD/√N

Mean +- (1.96 x SE) = Upper and lower confidence limit

95% confident that the true mean lies between the LCL and UCL

17
Q

What are the 4 assumptions in estimating population proportions

A

Sample randomly chosen
Independent observations
Proportions with characteristic not close to 0 or 1
np and n(1-p) are >5 (large sample)

18
Q

How do you calculate SE for proportions

A

√(p(1-p))/n = SE

p = proportion with characteristic
(1-p) = proportion without characteristic
19
Q

How do you calculate the lower and upper confidence limit

How do you use these values to find the confidence intervals for a proportion of the population

A

p +-(1.96 x √p(1-p)/n) = Upper and lower confidence limit

95% confident that the true mean lies between the LCL and UCL