Introduction to confidence intervals

what are confidence intervals and margins of error good for?

vitally important to interpreting political polls and surveys

key toold in inferential stats. for relating stats about our sample to the population of interest

1. confidence intervals

2. margin of error

3. confidence levels

margin of error

the degree of uncertainty around the relationship of our sample mean to the population mean, due to random sampling error.

how is the margin of error expressed as?

as a range of values below or above the sample mean

confidence level

percentage that indicates how confident we are that a population parameter lies within a specified margin of error

• for example, a 95% confidence level means that if we are conducting the sample survey 100 times, we would expect the true population value to fall within the margin of error in 95 of those surveys

what happens to the margin of error when analyzing subgroups in polls?

the margin of error for subgroups is larger due to smaller sample sizes, leading to less precision in estimates

T/F: you need to check for the normla distribution of your data before consstructive the margin of error

TRUE: these stats are built on an assumption of normality

(if the data is not normally distributed, the results will be innacurate)

3 reasons to undertand the steps when calculating the margin of error

1. to make informed decisions about the trade-offs for different confidence levels given your sample size and desired precision of esetimate

2. to accurately interpret the stats and identify any errors in their calculation and application to your study

3. even using excel’s “confidence.t” function to calculate confidence intervals will require you to enter the alpha level, standard deviation, and sample size into the function (GOOGLE SHEETS ODES NOT INCLUDE THIS FUNCTION)

2 key stats to calculate the margin of error

1. critical value

2. standard error

critical value

a test statistic that translates your chosen confidence level into a standardized score marking the difference from the sample mean to that level of probability

what do you need to know to find t-score critical value?

1. degrees of freedom

2. alpha leve and critical probability

standard error of sample proportions

• no meeaningful mean (categorical data)

• estimate of the standard error called Standard error of sample proportion

formula for the standard error of sample proportion

Margin of error = ________ * _________

Margin of error = Critical value * standard error of proportion