Quant2 - Inferential Statistics

What are inferential statistics?

methods for making statements about the population based on a sample

Example:

• sample of 10 from a population of 1000

• 3 men, 7 women

• what is the minimum and maximum number of in the population with 100% certainty?

• what would be a suggestion to make a more meaningful statement?

Minimum: 3

Maximum: 993

Suggestion: taking some risk of drawing the wrong conclusion is necessary to make meaningful statements about the population, because generalising with 100% certainty is useless

One of the conditions for making statements about a population based on a sample is using a representative sample:

• what type of sample is commonly used? and what is the sample selection (preferably) based on?

• what type of sample would be even better? what does this sample take into account?

commonly used: random sample

• based on sampling frame: a complete list of all units in the population from which units are drawn completely at random

even better: stratified random sample

• takes into account: proportions of different groups who might see things differently

Another condition for making statements about a population based on a sample is using the appropriate method:

• which 2 methods can be used?

• what do they test/estimate?

• what is the main difference between them?

1.  Hypothesis testing

Tests if an assumption about a population is likely to be true, by determining if the observed effect is statistically significant

2. Confidence intervals

Estimates a range of values that likely contains the true population parameter (like the mean or proportion)

Main difference:

• Hypothesis testing tells you if an effect exists (significance).

• Confidence intervals tell you where the true value likely lies (estimation).

What does the null hypothesis imply? And what purpose does it serve?

that there is no effect, no difference, or no relationship between variables in the population.

it serves as a statement which can be either rejected (meaning evidence suggests an effect or difference) or not rejected (meaning there’s not enough evidence to say otherwise).

When do you use a one-tailed test, and when do you use a two-tailed test?

One-tailed: when you have an idea in which direction an effect might go (either greater than OR less than)

Two-tailed: when you want to detect any difference, regardless of direction.

For hypothesis testing: when are critical values useful, and when are p-values useful?

Critical values are useful for understanding and visualising hypothesis testing:

• they help visualize the “threshold” where we stop believing the null hypothesis

• show the logic of hypothesis testing step-by-step

P-values are a good alternative to critical values for real-world situations

• more flexible, informative, and easier to use, especially in software

• Same logic for all kinds of tests

• No complicated formulas

In the case of using p-values, when do you reject the null-hypothesis?

when p-value < (α) significance level