Quiz 2 - t Tests

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19 Terms

1
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  • what is a t-test?

    • what are the different types? (3)

  • an inferential statistics for determining if there is a difference between two means

  • dif types

    • one-sample t test

    • dependent-samples t test

    • independent-samples t test

2
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  • what is a one-sample t test?

    • give some examples.

  • difference between sample mean and population mean, i.e., a different between M and u

    • examples:

      • Is there a difference in SAT scores between Californians versus Americans?

      • Is there a different in conscientiousness between people in their 20s versus people in general?

      • Is there a difference in working memory capacity between those with ADHD versus the general population?

3
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  • what is a dependent-samples t test?

    • give some examples.

  • Difference between 2 samples that are related to each other; also known as paired- or related-samples t test

  • Examples

    • Is there an increase in test performance from before to after an academic intervention?

    • Is there a change in depression from before to after psychotherapy?

    • Is there a difference between a group’s language and math GPA scores?

4
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  • what is an independent-samples t test?

    • give some examples

  • difference between 2 samples that are unrelated to each other

  • examples:

    • is there a difference in test performance between those who did and did not have an academic intervention?

    • is there a difference in depression between those who did and did not receive psychotherapy?

    • is there a difference between two groups’ language GPA scores?

5
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how do you calculate all the different degrees of freedom of the different t-tests?

  • one-sample t test df: n-1

  • dependent-samples t test df: n-1

  • independent-samples t test df": n-2

6
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what assumptions are made related to t-tests?

  • all t tests assume normality in the population distrbution

    • t-tests are robust to a violation of thiss assumption, especially with samples sizes > 30. Values between -2 and +2 for skewness and kurtosis are acceptable for a normal univariate distribution

7
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what is an additional assumption made by independent-samples?

  • t tests have an additional assumption — the assumption of homogeneous variances i.e, that the dispersion of scores for one population is equal to the dispersion of scores in the other population

  • Levene’s test evaluates the homogeneity assumption for t tests and ANOVAs in SPSS. When you have heterogenous variances (i.e., when p < .05), that t test gives you Welch’s solution on the SPSS output to use instead

8
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what is effect size?

  • a measure of the magnitude of a relationship between variables

    • virtually any difference between groups is statistically significant with large enough samples but necessarily important

  • note: effect size informs if a statistically significant results is meaningful or important

9
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  • what is cohen'‘s d?

    • what are the different effect size categories?

  • a common measure of effect size for t tests.

  • Guidelines

    • x < .2 = trivial effect size

    • .2 < x < .5 = small effect size

    • .5 < x < .8 = medium effect size

    • x > .8 = large effect size

10
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what is a confidence interval?

  • a range with a probability that a parameter is included in that range

11
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how can you use confidence intervals for one-sample t tests?

  • You can use confidence intervals to calculate the population mean if you don’t have it

  • ex. 95% CI [42.76,48.76]

  • Interpretation: There is a 95% probability that the interval 42.76 to 48.76 includes the population mean

12
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how can you use confidence intervals for dependent t tests?

  • You can use confidence intervals to calculate the population mean change between samples

  • ex. 95% CI [1.22,3.65]

  • Interpretation: There is a 95% probability that the interval 1.22 to 3.65 includes the population mean change

13
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how can you use confidence intervals for independent t tests?

  • You can use confidence intervals to calculate the population mean difference between samples

  • ex. 99% CI [.41,.88]

  • Interpretation: There is a 99% probability that the interval .41 to .88 includes the population mean difference

14
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what factors affect significance?

  • DNA SAT

    • Difference between means

    • N

    • SD

    • alpha

    • one-versus two tailed test

15
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how does the difference between means affect statistical significance?

  • the greater the difference between means, the more likely you’ll have statistical significance

  • e.g., a larger difference between means = larger numerator = larger t stat (more likely to exceed the critical value in the table of critical values and therefore more likely to be statistically significant

16
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How does sample size affect statistical significance?

  • the greater the sample size, the more likely you’ll have statistical significance. Increasing sample size increases power.

  • e.g., larger N = larger t (larger test statistic). Again, a larger test stat is more likely to exceed the critical value in the table of critical values and therefore more likely to be statistically significant

17
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how does SD affect statistical significance?

  • the greater the standard deviation, the less likely you’ll have statistical significance

  • note: the bottom pair of distributions is most likely to statistically significant even though each pair has the same mean difference

<ul><li><p>the greater the standard deviation, the less likely you’ll have statistical significance</p></li><li><p><strong>note: the bottom pair of distributions is most likely to statistically significant even though each pair has the same mean difference</strong></p></li></ul><p></p>
18
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how does the alpha affect statistical significance?

  • the larger the alpha (i.e., the larger the rejection region), the more likely you’ll have statistically significance

  • the more willing you are to make a T1 error, i.g., the higher the alpha, the more likely you’ll have significance

  • or, compare alpha .05 and alpha .01 critical values for any given df and you’ll see that the value for alpha 0.5 is smaller, i.e., easier for a test stat to exceed and be statistically significant

19
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how does the difference between one tail versus two tailed test affect statistical significance?