Inferential statistics

what is the null hypothesis

no difference between groups or variables equality if rejected there is a difference

what is statistical significance

degree of risk taken that the null hypothesis is rejected when it is actually true

what are inferential statistics used for

compare differences among two or more means or averages

give an example of inferential statistics

study effects of two teaching methods divide class at random into two groups

what are maps of chance

comparison of results with what we would expect by chance compare with models of chance

give an example of chance affecting results

coin tossing results deviate from 50 50 due to biased coin biased tosser or independent variable

how does inferential statistics help with chance vs independent variable

it never rules out chance but makes it less likely explanation ten heads in a row could happen by chance but not likely

what do tests of significance do

allow decisions about a population based on information from a sample test the null hypothesis

how does sample size affect accuracy of sample means

larger sample size increases accuracy minimum 30

what is probability

expressed as a proportion between 0 and 1 zero means certain not to occur one means certain to occur

what does p less than 0.05 mean

the probability of obtaining a given t score by chance is less than 5 in 100

how are probability values interpreted

greater than 0.05 result is not significant less than 0.05 result is significant less than 0.01 result is highly significant

what is the t test

measures significance of a difference between independent samples by comparing obtained difference with difference chance can produce compares the mean between two groups

what does the t test tell us

if 100 comparisons were made between control groups a t value this large would occur less than 5 times in 100 trials probably not the work of chance

what is a 95 percent confidence interval

range of values which contain the true scores at a probability of 95 percent

why is a narrower confidence interval better

it gives a more accurate inference to the population example improvement 50 percent with 95 CI 25 to 75 percent compared to 48 to 52 percent

what determines the selection of an appropriate inferential test

the scale of measurement the number of groups and whether measurements are from independent or related participants

what is the first factor in selecting a test

scale of measurement nominal ordinal interval or ratio

what is the second factor

number of groups used in the investigation one or more

what is the third factor

whether measurements were obtained from independent participants or related samples such as repeated measures

what is the fourth factor

assumptions involved in using a statistical test such as distribution of scores or minimum required sample size

what is anova used for

compare three or more groups using interval or ratio measures with dependent or independent groups

what is the first step to calculate anova

calculate the sample means for each sample and the mean for all sample data

what is the sum of squares of error sse

sum of squared deviations of each data value from its sample mean

what is the sum of squares of treatment sst

sum of squared deviations of each sample mean from the overall mean multiplied by one less than the number of samples

how do you calculate degrees of freedom

total df n minus 1 df treatment m minus 1 df error n minus m

how do you calculate mean square of error mse

sse divided by n minus m

how do you calculate mean square of treatment mst

sst divided by m minus 1

how do you calculate the f statistic

f equals mst divided by mse

what is the f test based on

differences between the means in relation to variability and size of the groups

what does a significant f test tell you

two or more groups differ by more than expected by chance

why use the f test

if you fail to get a significant f test differences are likely due to chance provides more protection against flukes of chance than series of t tests allows measurement of combined effects of two or more treatment variables interaction effects

what is two way analysis of variance

anova with two independent variables for example alcohol consumption and drinking history

what is an interaction effect

increase in coordination errors depends on special combinations of amount of alcohol and drinking history important because it can produce unexpected results

how does a t test help

decides statistical significance of differences between two groups

how does anova help

decides statistical significance of differences between more than two groups

what is chi square used for

decides whether a distribution deviates significantly from chance used with nominal scale independent participants two or more groups