Inferential Statistics

What is B and what does it tell us

1-B = power Probability of attaining a statistical significance Usually set at B = .20 so power = .80 20% chance of type II error and 80% chance to reject Ho

Inferential statistics relies on two concepts

1. probability 2. sampling error

Sampling error explains these assumptions:

1. random sample (all members of population have equal chance of occurring in the sample) 2. homogeneity of variance (samples have same amount of variability)

Parametric test assumptions

1. samples are randomly chosen from normally distributed populations 2. variance between samples is homogeneous (roughly equal variable) 3. data measured on interval or ratio scales Stronger tests

What is CI

Confidence interval range of scores with specific boundaries or confidence limits that should contain the population mean 95% CI means that you are 95% confident that the population mean will fall within a specified interval

Alternative hypothesis

H1 difference between means is not due to chance

Type II Error

accept Ho when it is false Conclude that no difference exists when a difference really does exist

Post Hoc power analysis

determine the likelihood that a type II error was committed when a study results in a non-significant finding need to know N, observe effect size and level of significance used

degrees of freedom

number of values/components free to vary within a set of data each statistical test specifies how to calculate the df associated with that test

Type I Error

reject Ho when it is true conclude that real differences exist when it actually doesn't 5% chance of type I error, 95% sure you can reject Ho

What is sampling error

tendency for sample values to differ from actual population values

Null hypothesis

Ho Differences between means is due to chance Compare the p-value to predetermined level of significance to determine whether null hypothesis is rejected or accepted

Directional hypothesis

critical region defined by critical value at one end of the curve one tailed test more power

Non directional hypothesis

critical region defined by two critical values two tailed test less power

Priori power analysis

estimate sample size need to know level of significant, expected effect size and desired power

What is probability

likelihood that any one event will occur, given all possible outcomes represented by p

What are the four determinants of statistical power

1. signifiance criterion - making standard for rejecting Ho more rigorous by lowering alpha reduces chance of type I error and increases chance of type II error 2. variance (s2) - power increases as variance decreases 3. sample size (n) - power increases with sample size increase 4. effect size - power increases the larger the effect size

What is inferential statistics?

Allow us to estimate population characteristics from sample data Requires that we make certain assumptions about how well the sample represents the larger population

Statistical vs. clinical significance

results can yield statistical significance and not clinical significance

Non parametric test assumption

useful when normality and homogeneity of variance not satisfied can be used with very small samples data measured on normal or ordinal scales