SPSS & T-Tests

two ways we calculated z

• z score for a single raw score

  • need x, μ, and σ

    • (or x, M, and s)

  • Can look at % of scores above and below this z value using the

    table

• z score for a sample (n>1)

  • need M, μ, σ, n

  • First step - calculate SEM (σM)

  • Second step - calculate z

  • can also find % above or below

significant

• this refers to the score (the mean) being “unusual” - the probability of it occurring is SMALL

• if you have a significant finding:

  • The zobt is BEYOND the zcrit

    • larger than 1.96 or 2.58

    • smaller than -1.96 or -2.58

  • The p is SMALLER than your alpha

    • p < .05 or p < .01

• if you have a nonsignificant finding:

  • The zobt is NOT beyond the zcrit

    • smaller than 1.96 or 2.58

    • larger than -1.96 or -2.58

  • The p is LARGER than your alpha

    • p > .05 or p > .01

hypothesis testing problems

1. State the two outcomes (i.e., the null and alternative hypotheses)

2. Decide on alpha level (probability of false positive)—always do 2-tailed tests

3. Find critical value (or, rely on SPSS)

4. Find or calculate the observed value (usually through SPSS unless z or one sample t by hand)

5. Decide if results are significant or non-significant

6. Compute effect size* (if warranted or required). *SPSS will give you this

7. Communicate your results

steps illuminated

• Remember: z-tests and all t-tests are fundamentally the same

• A difference between two groups divided by some measure of variability (or, a signal-to-noise ratio)

1. Two possible, black and white, outcomes

   • Null hypothesis (H0): nothing changed

   • Alternative hypothesis (H1): something changed, there’s a difference between the two groups

2. Decide on alpha level (probability of making a false positive)

   • We only will do two tailed tests, so reject extremely high or low values. Common alpha levels are .05 and .01

3. Find critical values (if doing it by hand)

   • This is what the z- and t-tables are for. We will largely rely on SPSS telling us what level of significance our results are

     • for z - it’s +/-1.96 and +/-2.58

       • for t - you look it up IF you are doing a one-sample t test by hand

       • for t tests on SPSS - you don’t need a critical value - you read the p-value

4. communicate effect size

5. communicate results:

   • Write a short paragraph that: describes the variables, gives the descriptive statistics, and then the inferential statistic (plus effect size, if needed). For instance:

     • We measured reaction time in seconds for participants to complete the task. We compared the performance of those who took caffeine (M = 6.75 s, SD = 0.98) to those who did not (M = 5.64 s, SD = 0.86). Using an independent samples t-test, this is a significant difference, t(43) = 2.43, p = .021, r2 = .12.

remember - we set a standard to test against alpha of .05 or .01

• So we are saying - we want to find something or find some difference that occurs less than 5 times out of 100 (.05) or less than 1 time out of 100 (.01)

• Our alpha level is set and we are using THAT as our comparison point

• If we find something LESS than alpha - the difference is SIGNIFICANT and we reject the null hypothesis

• If we find something GREATER than alpha - the difference is NOT significant and we fail to reject the null hypothesis

• so this is what we are talking about with p-values

effect size

• p-values are good - but can be flawed in how we think about them

• Most journals nowadays want you to report the p value AND the appropriate effect

  size

• Why?

  • they are unaffected by sample size (n)

  • used for comparisons (like in a meta analysis)

  • don’t have a set “cut point” (like an alpha of .05)

  • use “small”, “medium” and “large” designations

  • often used in conjunction with confidence intervals (Wed’s class)

  • different calculations of effect sizes depending on what statistic you do

• Significance asks is there an effect?

• effect size asks how big is the effect?

type I error

• false positive

  • Reject H₀ but there is no effect

  • noticing something that isn’t there

type II error

• false negative

  • Fail to reject H₀ but an effect exists

  • missing something that is there

power

• Power is the ability to reject the null hypothesis when the null hypothesis should be rejected

• in other words - the more power, the less likely you are to make a Type II error

• there are mathematical parts to this - related to alpha

• But I want you to think of it conceptually - that is:

• you need to increase signal or decrease noise

specific ways to increase power

• increase your sample size (n)

• increase the effect size

• reduce your measurement error

• decrease your noise by increasing your internal validity

• BUT

  • you don’t want too much power - because that leads to very sensitive tests (in other words, you might find an effect that has no real world practical

    meaning)

how can we tell if our sample is DIFFERENT from the population?

• z-test

• SD came from population

how can we tell if our sample is DIFFERENT from the population?

• one sample t-test

• SD came from sample, not population

how do we test if our groups are different?

• independent samples t-test

• has experimental & control groups (different groups)

how do we know if there are differences from pre to post training?

• dependent samples t-test

• same group tested twice

z-tests

• This uses the basic z formula

• BUT you have to account for the

  sample size

• you do that by calculating the SEM

• you put the SEM in the z formula

• instead of the standard deviation

• do these by hand

when you have a one sample experiment:

• Always need to know μ but…what else do you have?

• Know σ? Use a z-test

• No σ? Use a t-test

one sample-tests

• Can do by hand

• like the z-test

• Know σ? Use a z-test

• No σ? Use a t-test

• OR do on SPSS

  • only IF you have the raw data