Probability & Sampling

Sampling Distribution

the plotted distribution of a sample statistic across many samples

Central Limit Theorem

If repeated independent random samples of size N are drawn from a population, then as N grows large, the sampling distribution of sample means becomes approximately normal

Standard Error

the standard deviation of the sampling distribution

z-score

tells you how many standard deviations a value sits from the mean

Point Estimate

the best guess of our parameter value

confidence interval

a set of numbers around the point estimate that we believe the true parameter exists

Confidence Level

The probability the confidence interval produces an interval that contains the parameter (usually 95%)

df

the number of values in the final calculation of a statistic that are free to vary (n-1)

t-distribution

a probability distribution used to estimate population parameters when sample sizes are small and the population standard deviation is unknown

null hypothesis

States there is no effect or relationship between variables; any observed difference is put down to chance

p-value

the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true.

t-statistic

a standardized value that quantifies the difference between an observed result and a reference value (often the null hypothesis) relative to the variability in the data

t-test

used to determine whether the means of two groups are significantly different from each other

when to use t-statistic

smaller samples; standard deviation is unknown; when you want to compare the mean of one sample to a known value or the means of exactly two groups; standard error is unknown, so a penalty in df is used

when to use a z-statistic

larger sample sizes; standard deviation is known; when comparing sample mean to population; when comparing sample mean of exactly 2 groups; assesses difference in proportions; SE has a set range of possibilities

Wider distribution

smaller sample gets in t-statistic