Statistics

What is the purpose of estimation in statistics

To estimate unknown population parameters using sample statistics and confidence intervals

What is a confidence interval CI

A range of plausible values for a population parameter calculated from a sample

How do you interpret a 95 percent confidence interval

If we repeated the study many times 95 percent of the resulting intervals would contain the true population value

What impacts the width of a confidence interval

Sample size confidence level and data variability

What is the standard error SE

It measures how much a sample statistic varies from sample to sample smaller SE means more precision

When do we use the t-distribution instead of normal

When estimating means from small samples or when the population standard deviation is unknown

What does margin of error mean

The range above and below the estimate in a confidence interval calculated from SE times critical value

Formula for a CI for a mean

x̄ ± t star times SE

What are the steps of hypothesis testing

State hypotheses check conditions calculate test statistic find p value compare to alpha conclude

What does a p-value represent

The probability of getting a result at least as extreme as the observed one assuming the null hypothesis is true

What does it mean to reject the null hypothesis

There is enough evidence to support the alternative hypothesis

What is a Type I vs Type II error

Type I is rejecting a true null Type II is failing to reject a false null

What is the purpose of explanation in stats

To explore why differences exist between groups based on study design

What is the difference between causal and associational explanation

Causal is due to experimental control associational is based on observed patterns

What do you write for formal hypotheses using symbols

H0 mu1 equals mu2 or H0 p1 equals p2 alternatives use not equal greater than or less than

Why is context important in interpreting statistical results

Because statistical significance does not always mean practical importance

What is ANOVA used for

To compare means of three or more groups to see if at least one is different

What is the F-ratio

It compares between group variance to within group variance

What are the key conditions for ANOVA

Independent observations approximately normal distributions and similar standard deviations

What do we conclude if the p-value for ANOVA is small

At least one group mean is significantly different

What is the purpose of using distributions in statistics

To model variability in data and make inferences from samples to populations

What are common types of data distributions

Categorical numerical and binary

What does relative risk compare

The proportion of one group experiencing an outcome compared to another

What does a risk ratio of one mean

There is no difference in risk between the two groups

What is regression used for

To describe the relationship between a response variable and one or more explanatory variables

What does the slope in regression mean

The average change in the response variable for each unit increase in the explanatory variable

What is the residual

The difference between the observed value and the predicted value

What does R squared tell us

The proportion of the variability in the response variable explained by the model

What is the goal of generalisation

To apply findings from a sample to the wider population

What is RMSE

Root mean squared error measures prediction error of a model

Why are random samples important in generalisation

They reduce bias and increase the representativeness of the sample

What is overfitting

When a model captures noise instead of the true relationship making it poor at prediction