Independent Samples ttest

1
Independent Samples t-test
2
Review of Tests Weve Learned So Far

• z-test and one-sample t-tests
• Used to compare one sample mean to a population
  mean or some other known value.
• More common Compare two (or more) sample means
  to each other
• Two general research strategies
• Two completely separate (independent) samples
• Two related (dependent) samples

3
Introducing the Independent Samples t-test

• Did mental imagery raise scores or are the
  differences due to chance (sampling error)?
• Or, do the samples come from the same population?

Pop1 µ?
Pop2 µ?
Sample1 Rote Memory M19
Sample2 Imagery M25
4
A Quick Word on Notation

• Use subscripts to designate to which group
  statistics and parameters belong
• n1, SS1, S21, M1, µ1
• n2, SS2, S22, M2, µ2

5
Setting the Statistical Hypothesis for Ind.
Samples

• For Two-Tailed (Directional) Tests
• H0
• H0 µ1 µ2 0
• Or
• H0 µ1 µ2
• H1
• H1 µ1 µ2 ? 0
• Or
• H1 µ1 ? µ2

6
Independent Samples t Ratio
is the standard error of the
mean difference.
where
7
Two Sample t-test Example

• Research Question Does mental imagery change
  memory scores?
• State Statistical Hypothesis
• H0 µ rote µ imagery
• H1 µ rote ? µ imagery

8
Two Sample t-test Example

• Group1 Rote Group2 Imagery
• 24 13 18 31
• 23 17 19 29
• 16 20 23 26
• 17 15 29 21
• 19 26 30 24
• Sample Descriptive Statistics
• Rote Group n110, S2117.78, SS1160,
  M119
• Imagery Group n210, S2222.22, SS2 200, M225
• Compute standard error of the mean difference

9
Two Sample t-test Example

• Set Decision Criteria
• df(n1-1)(n2-1)(10-1)(10-1)18
• If a.05 and two-tailed test, from t-table, tcrit
  2.101
• Reject Ho if tobtainedgt tcrit
• Compute test statistic (tobtained)
• Make Decision Reject HO
• Mental imagery memory scores are significantly
  higher compared to rote scores, t(18)-3.00,
  plt.05.

10
Setting Decision Criteria for a Directional Test
(one-tailed)

• Mental imagery improves memory scores.
• H0 µ1gtµ2 or H0 µ1-µ2gt0
• H1 µ1ltµ2 or H1 µ1-µ2lt0
• Where µ1Rote Group and µ2Imagery Group
• In this case, set decision criteria Critical
  region is in the lower tail of the distribution.
• df(n1-1)(n2-1)(10-1)(10-1)18
• If a.05 and one-tailed test, from t-table, tcrit
  - 1.734
• Reject Ho if tobtained falls within the critical
  region.

11
Setting Decision Criteria for a Directional Test
(one-tailed)

• Mental imagery decreases memory scores.
• H0 µ1ltµ2 or H0 µ1-µ2lt0
• H1 µ1gtµ2 or H1 µ1-µ2gt0
• Where µ1Rote Group and µ2Imagery Group
• In this case, set decision criteria Critical
  region is in the upper tail of the distribution.
• df(n1-1)(n2-1)(10-1)(10-1)18
• If a.05 and one-tailed test, from t-table, tcrit
  1.734
• Reject Ho if tobtained falls within the critical
  region.

12
Assumptions of the Independent Samples t-test

• Independent Observations
• Normality
• Homogeneity of Variance

13
How big is the effect?

• We can use Cohens d to estimate effect size