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
