Lec 5: Hypothesis, data collection and error

what does having a significance level or p value of 0.05 mean in words

willing to accept a 5% chance your results are due to random error

• risk of type 1 error or alpha

how to calculate power with beta

1-beta

what does power represent

the probability of correctly rejecting the null hypothesis when it is false

• 80% power implies a 20% chance of making a type 2 error

the higher the power…

the more sensitive the test is to detecting a true effect

if power is high,  the chance of making a type 2 error…

goes down

when you increase the sample size…

you increase power, sensitivity

• reduces alpha, beta

Link between Alpha and Beta

• decrease alpha from 5% to 1% increases the beta

• increasing the alpha from 5% to 10% decreases the beta but higher risk of a type 1 error

• larger effect size easier to detect a difference

• small effect size more difficult to detect a difference - so need to increase sample size or reduce beta

• increasing sample size reduces alpha and beta as increase
  precision

list the Basic Elements of Testing Hypothesis

1. state null and alternative hypothesis

2. choice of appropriate level of significance (α)

3. test statistic (formula): application of sample results in the formula to
   calculate the value of test statistic use for decision purpose

4. rejection region (critical region): based on alternative hypothesis and
   level of significance (α)

5. decision: decide whether or not reject null hypothesis

Underlying Assumptions for Testing of Hypothesis for Population Mean

• the sample has been randomly selected from the population or process

• the underlying population is normally distributed (or if not normally
  distributed, then n is large say greater than or equal to 30)

• population variance (σ²) either known or sample variance (s²)assumed to be approximately equal to population variance (σ²), when n is large

Potential Errors pic

as type 1 error decreases…

type 2 error increases

what are alpha and beta also used to calculate

• sample size

• power of the test (probability of find an effect if one exists)

• effect size

Statistical Testing purpose

used to determine the probability of error in the rejecting the null hypothesis

p value def

probability of finding an effect as large or larger than the observed effect

RESEARCH PROCESS steps

• generating the idea

• generating the hypothesis

• deciding on risk of Type 1 and Type 2 errors

• collecting the data

• analysing the data

• deciding whether the data supports us to reject the NULL HYPOTHESIS

• dissemination

• generating the idea for the next research project

which part of the hypothesis is the theory

conducts the study and puts forward an explanation for their predictions/findings

theory def/characteristics

interrelated set of constructs formed into propositions that specify the relationships among variables

• describes how and why variables are related

• can have a series of if-then statements
  

the p value is also rejected when..

its lower than the alpha