Inferential Statistics

What is inferential statistics

Inferring features of a pop by looking at a small sample

What do inferential statistics determine

The likelihood that a conclusion is true

Parametric stats

Groups of statistics that are related, follow Gaussian distribution

What are parametric stats defined by

Parameters

Parameters in parametric stats

Mean and standard deviation, t-tests, ANOVA, correlation, regression

Non-parametric stats

Non-normal distributions with extremely small sample sizes

Examples of non-parametric stats

Chi squared, Wilcoxin-ranking, and others

What are assumptions of statistical inference based on

Probability and sampling error

Probability

Study of random events

Range of probability

0 to 1

What do we use probability as

Means of prediction

Probability for an event that is certain to occur

1

Why is probability predictive

It reflects what SHOULD happen over the long run, not necessarily what WILL happen for any given trial

Once an event happens is it “probable”

No, it either happened as predicted or not

What does probability apply to

The proportion of time we can expect a given outcome to occur in the long run

How is probability used in research

To determine if observed treatment differences are likely to be representative of population differences or if they could have occurred by chance

How do we apply probability in a research sample

To predict/estimate what would happen to others in the population based on what happened to our sample

Goal of sampling

Sample has to be a good representation of the entire population

What must a sample be

RANDOM

What do we do with categorical data

Calculate proportions

What does a sampling distribution do

Shows how a statistics varies sample to sample

What is the sampling distribution

Getting different means from different samples

What makes a sampling distribution more accurate

More samples

Do we usually take more than one sample

No, just take a bigger one

Standard error of the mean

How far our sample mean is from pop mean

Standard error of mean formula

Standard deviation

How widely scattered measurements are

Standard error of the mean

Indicate the uncertainty around the estimate of the true population mean

Confidence Interval

Range of scores with specific boundaries (confidence limits) that SHOULD contain the population mean

Confidence interval formula

Most common CI

95%

Z-score for 95% CI

+ or - 1.96

Z-score for 99% CI

2.576

Type I error

False positive

Type II error

False negative

Statistical significance

Results of an analysis are unlikely to be due to chance at a specified probability level

What happens if your results are statistical significance

You reject the null hypothesis

How do you format CI result

( x% CI: x - x )

Significant difference/effect

If the evidence/data show that it is unlikely that chance is causing observed differences

Not significance different

There isn’t enough evidence to reject the null hypothesis

Another name for Type I error

Alpha

Explain type I error in terms of significance

We conclude that a real difference exist when he differences are due to chance

Calling them “statistically significant”

Another name for type II error

Beta

Explain type II error in terms of statistical significance

Conclude that the differences are due to chance when the samples are truly different

Calling results “not statistically significant”

What must happen to determine the probability of committing a Type I error

Must be a standard set for rejecting the null hypothesis

Level of significance

Alpha value

What is the level of significance

The probability that an observed difference did occur by chance is determined by statistical tests

What does the selected alpha level define

Maximal acceptable risk of making a Type I error, if we reject Ho

What does an alpha level of 0.05 mean

You are willing to accept a 5% chance of incorrectly rejecting the null hypothesis

What does beta denote

Probability of making Type II error, probability of failing to reject a false null hypothesis

Discrete values

Have only one of a limited set of values, can only be expressed as whole numbers

Continuous values

Have a range and may take any value within that range

Nominal data

No implied order, unranked; categorical

Ordinal data

Numerical ranked data; based on some criteria

Interval data

No meaningful 0 (e.g. temp)

Ratio data

Meaningful zero (e.g. height)