Confidence and uncertainty

probability

likelihood of something happening

probability (a priori)

the probability of an event based on logical reasoning or theoretical analysis, before any empirical data or observation is considered

probability (a posteriori)

the probability of an event occurring after taking into account observed data or evidence.

posteriori probability and sampling distribution

If we know freq distribution - can calculate proportion of values observed within a specified range of values

central limit theorem

states that the sampling distribution of the mean will be approximately normally distributed, regardless of the shape of the population distribution, as long as the sample size is sufficiently large.

bell shape

calculating probabilities from normal distribution

need to find z value by doing x - mean / std

look at table to find z value

less than = area under the table

greater than = area under the table - 1

between = bigger z value (larger area) - smaller z value (smaller area)

total area under the curve = 1

estimating the standard deviation of the sample means

estimated by the standard error

confidence intervals for the mean

range of values - to show uncertainties

the larger the sample size, the smaller the confidence interval

to calculate it need to know how variable means are need to know mean of means from sample

the value of t depends on sample size and chosen level of confidence

the bigger the t value is the bigger the confidence level is