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Statistics > Confidence and Significance > Flashcards

Confidence and Significance Flashcards

1
Q

What is statistical inference?

A

Drawing conclusions about the underlying population from the sample

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2
Q

We compute the ________ in the sample to estimate the ___________ in the population.

A

▪️Sample
▪️Parameter

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3
Q

What is μ?

A

The population mean

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4
Q

What is x̄?

A

The sample mean

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5
Q

If we take more than one sample, why might x̄ differ?

A

▪️Random variation/sampling error
▪️Systematic error (bias)

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6
Q

What are the two main types of error?

A

Random error and systematic error

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7
Q

What is random error?

A

An unpredictable error due to unknown factors. It can go in either direction

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8
Q

What is a systematic error (bias)?

A

A consistent and repeated underestimate OR overestimate of the true value due to factors that can be traced in the experimental design

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9
Q

What is the central limit theorem?

A

Given a sufficiently large amount of repetitions, the sampling distribution will approximate the normal distribution (Galton board)

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10
Q

What is the sampling distribution of the mean?

A

The distribution of all the sample means taken from the same population, plotted into a histogram

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11
Q

In a normal distribution, what percentage of observations are ±1 SD from the mean?

A

68%

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12
Q

In a normal distribution, what percentage of observations are ±1.96 SD from the mean?

A

95%

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13
Q

In a normal distribution, what percentage of observations are ±2.58 from the mean?

A

99%

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14
Q

Will the sampling distribution of the mean approximate the normal distribution if the population parameter is not normally distributed?

A

Yes

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15
Q

What does the mean of the sampling distribution equal?

A

The mean of the population

mean(x̄) = μ

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16
Q

What does the mean of the population equal?

A

The mean of the sampling distribution

μ = mean(x̄)

17
Q

If you have the variance of the samples means, how do you get the population variance?

A

Times it by the sample size

variance(x̄) x n = σ^2

18
Q

If you have the population variance, how do you work out the variance of the samples means?

A

Divide it by the sample size

variance(x̄) = σ^2 / n

19
Q

What is the standard error?

A

The standard deviation of the sample distribution

SE = σ / √n

20
Q

If you have the variance, how do you work out the standard deviation?

A

Take the square root

21
Q

If you have the standard deviation, how do you calculate the variance?

A

Square it

22
Q

If the variability of the distribution is smaller, what does that mean for the standard error?

A

There will be a smaller SE and thus greater precision

23
Q

If you take larger samples, what does this mean for the sample error?

A

There will be a smaller SE and thus greater precision

24
Q

What is the main problem with estimating the population parameters in research?

A

We usually only have one sample so we have to approximate the sampling distribution

25
Q

How do you interpret the 95% confidence interval?

A

We will capture the true population mean 95% of the time in the long run, if we repeat the experiment many times (we can say with 95% confidence that it is in this interval)

26
Q

What is the point estimate?

A

The estimate of the parameter of interest

27
Q

How do you calculate the 95% CI?

A

[x̄ - 1.96SE, x̄ + 1.96SE]

28
Q

In what situations would you use a 99% CI and what would you multiple the SE by to get this?

A

In ‘life and death’, 2.58

29
Q

What test and value would you use for the CI if the sample size was smaller than 30?

A

The t-distribution (using t-values instead of z-values)

30
Q

What does a wider confidence interval indicate?

A

Increased confidence (NOT accuracy)

31
Q

What is the sampling distribution?

A

The distribution of estimated values for a parameter, based on random samples of the same size from a population

32
Q

What is the SD of the sampling distribution equal to?

A

The SD of the population divided by the square root of the sample size

33
Q

The _______ sample mean provides a _______ _________ of the population _______ mean.

A

▪️statistic
▪️point estimate
▪️parameter

Statistics (12 decks)

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