Confidence and Significance Flashcards
What is statistical inference?
Drawing conclusions about the underlying population from the sample
We compute the ________ in the sample to estimate the ___________ in the population.
▪️Sample
▪️Parameter
What is μ?
The population mean
What is x̄?
The sample mean
If we take more than one sample, why might x̄ differ?
▪️Random variation/sampling error
▪️Systematic error (bias)
What are the two main types of error?
Random error and systematic error
What is random error?
An unpredictable error due to unknown factors. It can go in either direction
What is a systematic error (bias)?
A consistent and repeated underestimate OR overestimate of the true value due to factors that can be traced in the experimental design
What is the central limit theorem?
Given a sufficiently large amount of repetitions, the sampling distribution will approximate the normal distribution (Galton board)
What is the sampling distribution of the mean?
The distribution of all the sample means taken from the same population, plotted into a histogram
In a normal distribution, what percentage of observations are ±1 SD from the mean?
68%
In a normal distribution, what percentage of observations are ±1.96 SD from the mean?
95%
In a normal distribution, what percentage of observations are ±2.58 from the mean?
99%
Will the sampling distribution of the mean approximate the normal distribution if the population parameter is not normally distributed?
Yes
What does the mean of the sampling distribution equal?
The mean of the population
mean(x̄) = μ
What does the mean of the population equal?
The mean of the sampling distribution
μ = mean(x̄)
If you have the variance of the samples means, how do you get the population variance?
Times it by the sample size
variance(x̄) x n = σ^2
If you have the population variance, how do you work out the variance of the samples means?
Divide it by the sample size
variance(x̄) = σ^2 / n
What is the standard error?
The standard deviation of the sample distribution
SE = σ / √n
If you have the variance, how do you work out the standard deviation?
Take the square root
If you have the standard deviation, how do you calculate the variance?
Square it
If the variability of the distribution is smaller, what does that mean for the standard error?
There will be a smaller SE and thus greater precision
If you take larger samples, what does this mean for the sample error?
There will be a smaller SE and thus greater precision
What is the main problem with estimating the population parameters in research?
We usually only have one sample so we have to approximate the sampling distribution
How do you interpret the 95% confidence interval?
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)
What is the point estimate?
The estimate of the parameter of interest
How do you calculate the 95% CI?
[x̄ - 1.96SE, x̄ + 1.96SE]
In what situations would you use a 99% CI and what would you multiple the SE by to get this?
In ‘life and death’, 2.58
What test and value would you use for the CI if the sample size was smaller than 30?
The t-distribution (using t-values instead of z-values)
What does a wider confidence interval indicate?
Increased confidence (NOT accuracy)
What is the sampling distribution?
The distribution of estimated values for a parameter, based on random samples of the same size from a population
What is the SD of the sampling distribution equal to?
The SD of the population divided by the square root of the sample size
The _______ sample mean provides a _______ _________ of the population _______ mean.
▪️statistic
▪️point estimate
▪️parameter
