Hypothesis Testing

Research Methods and Data Analysis

what does sampling distribution do?

allows us to assess the probability of obtaining a particular score from the population

what are p-values?

significance levels that determine how likely the obtained result would occur if the null hypothesis is true

what are critical values?

a specific value in the sampling distribution that must be obtained for the p-value to be significant

standard levels to evaluate the null hypothesis?

0.05 and 0.01

how to report p-values?

e.g, p < .05 p< .01

one-tailed vs two-tailed tests?

one-tailed specify the direction

two-tailed are non-directional

what are the steps for hypothesis testing?

1. state hypotheses: for H0 and H1

2. convert score to Z score: X-mean/ SD

3. compare the obtained value with the critical value of ± 1.96

4. make statistical decision

5. write up results in APA format

what is the format for reporting the results in APA format?

we can(not) conclude that the individual observation did not come from a population of ——, Z=___, p(ns) or p<____.

when is a result statistically significant?

if the obtained value is larger than the critical value, meaning you should reject the null hypothesis (H0)

when is a result not statistically significant?

if the obtained value is smaller than the critical value, failing to reject the null hypothesis (H0)

null vs alternative hypothesis?

H0= null hypothesis: X= population mean

H1= alternative hypothesis: X doesn’t= population mean

when to use central limit theorem?

when SD is known, to obtain the sampling distribution of the mean when the H0 is true

standard deviation= standard error: SD/ √N

what are the steps for hypothesis testing when standard deviation is known?

1. state hypotheses

2. compute standard error: SD/ √N

3. convert the sample mean (population mean) to a Z score: X-mean/ SE

4. compare the obtained value with the critical value ± 1.96

5. make statistical decision

6. write up the findings in APA format

what is the format for reporting results in APA format when the SD is known?

we can(not) conclude that the sample mean did(not) come from a population of ___-, Z=____, p(ns) or p<___.

if significant, state how the sample differs (pps from sample have higher/lower scores {M= mean value} than scores in the population {M= mean value}.

when to use a one sample t-test?

when the SD is unknown, value is evaluated with a T table

s² is an estimate of SD², the sampling distribution of s² is positively skewed

what are the steps for hypothesis testing when standard deviation is unknown?

1. state hypotheses

2. compute estimated standard error: s/√N

3. convert score to t score: X-mean/ estimated SE

4. compute degrees of freedom (df: N-1) : number of independent information remaining after estimating one or more parameters

5. look t_critical (replaces ± 1.96) and make a statistical decision

6. write up findings in APA format

what is the format for reporting results in APA format when the SD is unknown?

we can(not) conclude that the sample mean did(not) one from a population of ____, t(df)=____, p(ns) or p<___.

if significant, state how the sample differs (pps from sample have higher/lower scores {x̄= mean value} than scores in the population {μ= mean value}).

what is a confidence interval?

estimate the population mean from the sample mean, it specifies with a level of confidence, the range of scores in which the population mean lies

what are the steps for computing confidence intervals of the mean?

1. compute the sample mean and standard deviation

2. compute estimated standard error: s/√N

3. compute degrees of freedom: N-1

4. look up critical t

5. compute CI: 𝑋̄ ± 𝑡𝑐𝑖𝑟𝑖𝑡𝑐𝑎𝑙 ( 𝑠 / √𝑁 ) make sure to do one sum + and the other -

6. write up findings
   

how to write up findings for confidence intervals?

we are ___% confident that the mean number of _____ is between ___ and ____

what does making the wrong statistical error lead to?

type 1 errors: the probability of rejecting the null hypothesis, given that it is true. designated as a (.05, .01). a false positive

or

type 2 errors: the probability of failing to reject the null hypothesis, given that it is false. designated as (β). a false negative

what is power?

the ability to find statistically significant results

it is measured on a scale from 0 to +1

ideally want power to be around .8: then there is an 80% chance of correctly rejecting a false null hypothesis

what are the factors affecting power?

sample size: if this increases, the SE is reduced and power increases

effect size: (degree to which H0 is false) if increases, so does power

alpha level: (significance level) if the value of alpha increases, power also increases