exam review: confidence intervals

CI

• all else being equal, a higher confidence level will lead a wider confidence interval

• more likely to include the mean in there → but less precise

Mathematically, it means this:

• if we were to do this experiment over and over for 100 times → a 95% CI means that our “mean difference” will be between 1.3385 and 3.2615 95 times out of 100.

  • if we did it 500 times → we would get a mean difference in that range 475 times out of 500.

• If we did a 90% CI → our “mean difference” would be in a smaller range (more like 1.29 and 3.18) and we would get a number in that range 90 times out of 100.

  • if we did it 200 times → we would get a mean difference in that range 180 times out of 200.

quick hits

• Effect sizes - read off the SPSS printout, know the ranges for interpretation for values of Cohen’s d

• Alpha level (usually .05 or .01) will always be given in the

  question.

  • Remember → it’s labeled as “Two-sided p” on SPSS

  • numbers less than .05 (or .01) → would be significant

  • numbers greater than .05 (or .01) → would be nonsignificant

• One Sample t-test

  • if you get raw data → use SPSS

  • if you are only given a sample mean & sample standard deviation, and a. population mean → you must do it by hand using the appropriate formulas.

  • If you do it by hand → how do you tell what the critical value is

    and whether it’s significant? - need the t test tables and the df

z-test for a sample

• You have no raw data

• You have:

  • the population mean (µ) & the population standard deviation (σ)

  • You have the sample mean (M) only

one sample t-tests

• You might have raw data

• You have:

  • the population mean (µ) only

  • If you don’t have raw data, you have the sample mean (M) & the sample standard deviation (s)

independent samples t-test

• You have two groups of different people (two samples)

• You have:

  • scores for group 1 & scores for group 2

  • You are testing if the groups are different

dependent samples t-test

• You have one group of people (one sample)

• You have:

  • pre or before scores for each person & post or after scores for each person

  • You are testing if the intervention made pre and post scores different

z-tests remember:

find that z-score in the table (+/-) and look for the proportion under the curve that you need

one sample t-test when you do them by hand

• a) find alpha

• b) find df

• c) look for the crit t value

• d) compare the t you calculated to the critical one

• e) if calculated is bigger → it’s significant

• f) everything listed as positive but same for negative t’s

reminder about effect size

• small < .20

• .20 < medium < .80

• larger > .80

• two steps:

  • what is the numerical value? (take the absolute value)

  • what size is it?