estimation: confidence intervals

if its significant (calculation by hand)

• Your obtained statistic is BEYOND the critical value that is found on the table (or memorized for z-tests). Generally it’s a BIG number - and would be represented by the blue arrows in the “region of rejection”

• Another phrase is that you “reject the null hypothesis”

• This means that the probability is smaller or LESS than the set alpha If you are doing it by hand, you would determine that the value is beyond the critical value from the table, and you would write p < .05 or p < .01

if its significant (using SPSS)

• Your obtained statistic is still BEYOND the critical value - but you don’t need to look up the critical value.

• You will look at the p value given. If it is smaller than your alpha (.05 or .01), then it is significant. You write the exact value of p as reported on SPSS (p = _____)

if its not significant (calculations by hand)

• Your obtained statistic is NOT beyond the critical value that is found on the table (or memorized for z-tests). Generally it’s a relatively small value - and would be represented by the red arrow which is NOT in the region of rejection If you are doing it by hand calculations

• Another phrase is you fail to reject the null hypothesis

• This means that the probability is GREATER than the set alpha. If you are doing it by hand, you would determine that the value is not beyond the critical value from the table, and you would write p > .05 or p > .01 that means the probability is BIGGER than your set alpha.

if its not significant (using SPSS)

• Your obtained statistic is still NOT beyond the critical value but you don’t have to look up the critical value. If you are using SPSS

• You will look at the p value given. If it is larger than your alpha (.05 or .01), then it is not significant. You still write the exact value of p as reported on SPSS (p = _____)

interpretation of confidence intervals

• We determine how confident we would like to be (80%, 90%, 95% and 99% are common values)

  • What happens to size of interval as we increase confidence

    • Bigger numbers mean a “wider net”

    • Smaller numbers mean “more precision”

• A confidence interval shows how many times out of 100 when we do this same experiment would the true population mean lie within the interval

so cofidence intervals tell us (one sample t-test)

 in a one sample t-test → the interval represents where the upper and lower bounds are for the population mean (µ)

so cofidence intervals tell us (independent samples t-test)

 in an independent samples t-test → the interval represents the upper and lower bounds for the mean difference between group 1 and group 2

so cofidence intervals tell us (dependent samples t-test)

in a dependent samples t-test - the interval represents the upper and lower bounds for the mean difference between time 1 and time 2