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Comparing Two Means: One-sample & Paired-sample t -tests

Comparing Two Means: One-sample & Paired-sample t -tests. Lesson 13. Inferential Statistics. Hypothesis testing Drawing conclusions about differences between groups Are differences likely due to chance? Comparing means t -test: 2 means Analysis of variance: 2 or more means ~.

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Comparing Two Means: One-sample & Paired-sample t -tests

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  1. Comparing Two Means: One-sample & Paired-samplet-tests Lesson 13

  2. Inferential Statistics • Hypothesis testing • Drawing conclusions about differences between groups • Are differences likely due to chance? • Comparing means • t-test: 2 means • Analysis of variance: 2 or more means ~

  3. Comparing 2 means: t-tests • One-sample t-test • Is sample likely from particular population? • Paired-Sample t-test • 2 dependent (related) samples • Independent-samples t-test • 2 unrelated samples ~

  4. The One-sample t-test • Evaluating hypothesis about population • taking a single sample • Does it likely come from population? • Test statistics • z test if s known • t test if s unknown ~

  5. t statistic

  6. Example: One-sample t-test • Survey: college students study 21 hr/wk • Do Coe students study 21 hrs/week? • Select sample (n = 16) • s unknown • Nondirectional hypothesis: • H0 : m = 21; H1 : m¹21 • reject H0 if increase or decrease • PASW/SPSS: Test value = 21 • Assumed from H0 ~

  7. PASW One Sample T Test • Menu • Analyze • Compare Means • One-Sample T Test • Dialog box • Test Variable(s) (DV) • Test Value (value of m testing against) • Options (to change confidence intervals) ~

  8. PASW Output *1-tailed probability: divide Sig. 2-tailed by 2

  9. Paired-Samples t-tests • 2 samples are statistically related • Less affected by individual differences • reduces variance due to error • Repeated-measures • 2 measurements on same individual • Matched-subjects • Match pairs on some variable(s) • Split pairs into 2 groups ~

  10. Difference Scores • Find difference between each score • D = X2 - X1 • Requires n1 scores equal n2 scores • Calculate mean D • And standard deviation of D • ~

  11. Repeated-measures • 2 measurements of same individual • Pretest-posttest design • measure each individual twice • pretest  treatment  posttest • compare scores ~

  12. Matched-subjects • Match individuals on important characteristic • individuals that are related • IQ, GPA, married, etc • Assign to different treatment groups • each group receives different levels of independent variable ~

  13. Assumptions: Related Samples • Population of difference scores is normal • Observations within each treatment independent • scores for each subject in a group is independent of other subjects scores ~

  14. Related-samples Hypotheses • Nondirectional • H0: m D= 0 • H1: m D 0 • Directional • H0: m D>0 • H1: m D< 0 • Remember: it depends on the direction of the prediction ~

  15. Sample Statistics • Mean difference • Mean for single sample

  16. Standard Deviation: Related-samples Single sample

  17. Estimated Standard Error • Calculate same as single sample • use standard deviation of difference scores

  18. Test Statistic • Related-samples t test • Since mD= 0

  19. Example • Is arachnophobia limited to real spiders or is a picture enough? • Participants • 12 spider phobic individuals • Manipulation (IV) • Each person exposed to a real spider & picture of same spider at two different times • Outcome (DV): Anxiety

  20. PASW Paired-Sample T Test • Data entry • 1 column each DV • Menu • Analyze • Compare Means • Paired-Sample T Test • Dialog box • Paired Variable(s) (DV) • Options (to change confidence intervals) ~

  21. PASW Output

  22. Reporting the Results • On average, participants experienced significantly greater anxiety to real spiders (M = 47.00, SE = 3.18) than to pictures of spiders (M = 40.00, SE = 2.68), t(11) = −2.47, p < .05

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