PDU 207 Basic Statistics: Introduction to Hypothesis Testing

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PDU 207 Basic Statistics: Introduction to Hypothesis Testing

  1. 1. PDU 207 STATISTIK DASAR INTRODUCTION TO HYPOTHESIS TESTING SEMESTER GASAL 2015/2016 FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA KULIAH IX - 19 OKTOBER 2015
  2. 2. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati Mahasiswa memahami dasar logika dari uji hipotesis;01. ONE DAY OBJECTIVES 2 Mahasiswa mampu menyatakan hipotesis dan menentukan letak critical region;02. Mahasiswa mampu mendefinisikan dan melakukan perbandingan antara Type I error dan Type II error.03.
  3. 3. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati 5 LISTENING TO ADELE’S ALBUMS ICON CREDITS: Happy by Austin Condiff,
 Sad by Austin Condiff; from the Noun Project IMAGE CREDIT: hercampus.com/sites/default/files/2014/11/02/adele.jpg
  4. 4. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati 5 LISTENING TO ADELE’S ALBUMS ICON CREDITS: Happy by Austin Condiff,
 Sad by Austin Condiff; from the Noun Project IMAGE CREDIT: hercampus.com/sites/default/files/2014/11/02/adele.jpg DEPRESSION LEVEL DEPRESSION LEVEL 32 67
  5. 5. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati 6 LISTENING TO ADELE’S ALBUMSICON CREDITS: Happy by Austin Condiff,
 Sad by Austin Condiff; from the Noun Project IMAGE CREDIT: hercampus.com/sites/default/files/2014/11/02/adele.jpg DEPRESSION LEVEL DEPRESSION LEVEL 32 67 1. The change of pattern was produced by the random forces of chance 2. The change of pattern was created by
 a deliberate, systematic act
  6. 6. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati 6 LISTENING TO ADELE’S ALBUMSICON CREDITS: Happy by Austin Condiff,
 Sad by Austin Condiff; from the Noun Project IMAGE CREDIT: hercampus.com/sites/default/files/2014/11/02/adele.jpg DEPRESSION LEVEL DEPRESSION LEVEL 32 67 HYPOTHESIS TESTING 1. The change of pattern was produced by the random forces of chance 2. The change of pattern was created by
 a deliberate, systematic act MAKESURETHAT
  7. 7. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING A hypothesis test is a statistical method
 that uses sample data to evaluate a hypothesis
 about a population. 7 (Gravetter & Wallnau, 2010, p. 233)
  8. 8. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 8 THE UNKNOWN POPULATION The purpose of the research is to determine the effect of a treatment on the individuals
 in the population. That is, the goal is to determine what happens to the population
 after the treatment is administered. (Gravetter & Wallnau, 2010, p. 234)
  9. 9. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 8 µ = 32 ! = 10 T R E A T M E N T µ = ? ! = ? THE UNKNOWN POPULATION The purpose of the research is to determine the effect of a treatment on the individuals
 in the population. That is, the goal is to determine what happens to the population
 after the treatment is administered. (Gravetter & Wallnau, 2010, p. 234) THE KNOWN
 POPULATION THE UNKNOWN
 POPULATION
  10. 10. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 9 T R E A T M E N T THE SAMPLE IN THE RESEARCH STUDY The research study involves selecting a sample from the original population,
 administering the treatment to the sample, and then recording scores for the individuals
 in the treated sample. (Gravetter & Wallnau, 2010, p. 234-235)
  11. 11. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 9 T R E A T M E N T THE SAMPLE IN THE RESEARCH STUDY The research study involves selecting a sample from the original population,
 administering the treatment to the sample, and then recording scores for the individuals
 in the treated sample. (Gravetter & Wallnau, 2010, p. 234-235) POPULATION µ = 32 POPULATION µ = ? SAMPLE TREATED SAMPLE
  12. 12. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 10 THE FOUR STEPS (Gravetter & Wallnau, 2010, p. 234-235) 1.STATE
 THE HYPOTHESIS SET THE CRITERIA
 FOR THE DECISION2. 3. COLLECT DATA &
 COMPUTE SAMPLE
 STATISTICS 4.MAKE
 DECISION ICON CREDITS: Thought Bubble by irene hoffman, Compass by Dominique Vicent,
 Add Item by Creative Stall, Gavel by Creative Stall; from the Noun Project
  13. 13. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 11 THE FOUR STEPS (Gravetter & Wallnau, 2010, p. 236-237) 1.STATE
 THE HYPOTHESIS H0 Hypotheses Null: zero-effect, zero-change,
 zero-difference, or zero-relationship H1 Hypotheses Alternative: an effect, a change,
 a difference, or a relationship H0: µdepression level = 32 H1: µdepression level ≠ 32 } } ICON CREDIT: Thought Bubble by irene hoffman;
 from the Nount Project
  14. 14. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 12 THE FOUR STEPS (Gravetter & Wallnau, 2010, p. 237-239) 2.SET THE CRITERIA
 FOR THE DECISION 32 67determine exactly whether
 both values are “near”
 or “very different” BOUNDARIESALPHA LEVEL CRITICAL REGION a probability value that is used to define the concept of “very unlikely”
 in a hypothesis test composed of the extreme sample values that are very unlikely
 (as defined by the alpha level) to be obtained if the null hypothesis is true ICON CREDITS: Compass by Dominique Vicent,
 Happy by Austin Condiff, Sad by Austin Condiff; from the Noun Project
  15. 15. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 13 THE FOUR STEPS 2.SET THE CRITERIA
 FOR THE DECISION ALPHA LEVEL a probability value that is used to define the concept of “very unlikely”
 in a hypothesis test (Gravetter & Wallnau, 2010, p. 237-239)ICON CREDIT: Compass by Dominique Vicent;
 from the Noun Project
  16. 16. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 14 THE FOUR STEPS 2.SET THE CRITERIA
 FOR THE DECISION CRITICAL REGION composed of the extreme sample values that are very unlikely
 (as defined by the alpha level) to be obtained if the null hypothesis is true (Gravetter & Wallnau, 2010, p. 237-239)ICON CREDIT: Compass by Dominique Vicent;
 from the Noun Project
  17. 17. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 15 THE FOUR STEPS (Gravetter & Wallnau, 2010, p. 240) 3. COLLECT DATA &
 COMPUTE SAMPLE
 STATISTICS z = M-µ !M sample mean hypothesized
 population mean standard error
 between M and µ ICON CREDIT: Add Item by Creative Stall; from the Noun Project
  18. 18. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati THE LOGIC OF HYPOTHESIS TESTING 16 THE FOUR STEPS (Gravetter & Wallnau, 2010, p. 240-241) 4.MAKE
 DECISION TWO POSSIBLE OUTCOMES: 1. the data provide strong evidence that there is an effect, a change, a difference, or a relationship 2. the data do not provide strong evidence that there is
 an effect, a change, a difference, or a relationship REJECT H0 FAILED TO REJECT H0 ICON CREDIT: Gavel by Creative Stall; from the Noun Project
  19. 19. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati REPORTING THE RESULT 17 Mendengarkan lagu Adele memiliki efek yang signifikan terhadap
 tingkat depresi mahasiswa Fakultas Psikologi UAJ, z = 2,86, p < ,05 Mendengarkan lagu Adele tidak memiliki efek yang signifikan terhadap tingkat depresi mahasiswa Fakultas Psikologi UAJ, z = 2,86, p > ,05 REJECT H0 FAILED TO
 REJECT H0 ICON CREDITS: Happy by Austin Condiff,
 Sad by Austin Condiff; from the Noun Project IMAGE CREDIT: hercampus.com/sites/default/files/2014/11/02/adele.jpg
  20. 20. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati UNCERTAINTY AND ERRORS IN HYPOTHESIS TESTING Hypothesis testing is an inferential process,
 which means that it uses limited information
 as the basis for reaching a general conclusion. In this situation, there is always the possibility
 that an incorrect conclusion will be made. 18 (Gravetter & Wallnau, 2010, p. 244)
  21. 21. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati UNCERTAINTY AND ERRORS IN HYPOTHESIS TESTING 19 TYPE I ERROR 32 67the researcher is likely to conclude that
 the treatment does have an effect REJECT H0 w h e n i n f a c t … THE TREATMENT DOES NOT HAVE AN EFFECT (Gravetter & Wallnau, 2010, p. 244-245)ICON CREDITS: Happy by Austin Condiff,
 Sad by Austin Condiff; from the Noun Project
  22. 22. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati UNCERTAINTY AND ERRORS IN HYPOTHESIS TESTING 20 TYPE II ERROR 32 67the researcher is likely to conclude that
 the treatment does not have an effect FAILED TO REJECT H0 w h e n i n f a c t … THE TREATMENT DOES HAVE AN EFFECT (Gravetter & Wallnau, 2010, p. 245-246)ICON CREDITS: Happy by Austin Condiff,
 Sad by Austin Condiff; from the Noun Project
  23. 23. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati UNCERTAINTY AND ERRORS IN HYPOTHESIS TESTING 21 SELECTING ALPHA LEVEL (Gravetter & Wallnau, 2010, p. 246-247) The alpha level helps to determine the boundaries for the critical region
 by defining the concept of “very unlikely” outcomes.
 At the same time, the alpha level determines
 the probability of a Type I error. The primary concern when selecting an alpha level is
 to minimize the risk of a Type I error.
 Thus, alpha levels tend to be very small probability values.
  24. 24. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati UNCERTAINTY AND ERRORS IN HYPOTHESIS TESTING 22 SELECTING ALPHA LEVEL (Gravetter & Wallnau, 2010, p. 246-247)
  25. 25. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati DIRECTIONAL (ONE-TAILED) HYPOTHESIS TESTING In a directional hypothesis test, or a one-tailed test,
 the statistical hypotheses (H0 and H1) specify
 either an increase or a decrease in the population mean. That is, they make a statement about
 the direction of the effect. 23 (Gravetter & Wallnau, 2010, p. 256-258)
  26. 26. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati DIRECTIONAL (ONE-TAILED) HYPOTHESIS TESTING 24 THE FOUR STEPS 1.STATE
 THE HYPOTHESIS SET THE CRITERIA
 FOR THE DECISION2. 3. COLLECT DATA &
 COMPUTE SAMPLE
 STATISTICS 4.MAKE
 DECISION (Gravetter & Wallnau, 2010, p. 256-258)ICON CREDITS: Thought Bubble by irene hoffman, Compass by Dominique Vicent,
 Add Item by Creative Stall, Gavel by Creative Stall; from the Noun Project
  27. 27. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati DIRECTIONAL (ONE-TAILED) HYPOTHESIS TESTING 25 THE FOUR STEPS 1.STATE
 THE HYPOTHESIS H0: Tingkat depresi tidak bertambah H0: µ ≤ 32 H1: Tingkat depresi bertambah H1: µ > 32 (Gravetter & Wallnau, 2010, p. 256-258)ICON CREDIT: Thought Bubble by irene hoffman;
 from the Noun Project
  28. 28. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati DIRECTIONAL (ONE-TAILED) HYPOTHESIS TESTING 26 THE FOUR STEPS SET THE CRITERIA
 FOR THE DECISION2. (Gravetter & Wallnau, 2010, p. 256-258)ICON CREDIT: Compass by Dominique Vicent; from the Noun Project
  29. 29. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati DIRECTIONAL (ONE-TAILED) HYPOTHESIS TESTING 27 THE FOUR STEPS 3. COLLECT DATA &
 COMPUTE SAMPLE
 STATISTICS 4.MAKE
 DECISION TWO POSSIBLE OUTCOMES: 1. the data provide strong evidence that there is an effect, a change, a difference, or a relationship 2. the data do not provide strong evidence that there is
 an effect, a change, a difference, or a relationship (Gravetter & Wallnau, 2010, p. 256-258)ICON CREDITS: Add Item by Creative Stall,
 Gavel by Creative Stall; from the Noun Project
  30. 30. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati DIRECTIONAL (ONE-TAILED) HYPOTHESIS TESTING 27 THE FOUR STEPS 3. COLLECT DATA &
 COMPUTE SAMPLE
 STATISTICS 4.MAKE
 DECISION TWO POSSIBLE OUTCOMES: 1. the data provide strong evidence that there is an effect, a change, a difference, or a relationship 2. the data do not provide strong evidence that there is
 an effect, a change, a difference, or a relationship REJECT H0 FAILED TO REJECT H0 (Gravetter & Wallnau, 2010, p. 256-258)ICON CREDITS: Add Item by Creative Stall,
 Gavel by Creative Stall; from the Noun Project
  31. 31. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati CONCERNS ABOUT HYPOTHESIS TESTING 1. The focus of a hypothesis test is on the data rather than
 the hypothesis. When the null hypothesis is rejected, we are actually making a strong probability statement about the sample data, not about the null hypothesis. 2. Demonstrating a significant treatment effect does not necessarily indicate a substantial treatment effect. Statistical significance does not provide any real information about the absolute size of
 a treatment effect. Instead, the hypothesis test has simply established that the results obtained in the research study are very unlikely to have occurred if there is no treatment effect. 28 THE LIMITATIONS (Gravetter & Wallnau, 2010, p. 259-260)
  32. 32. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati CONCERNS ABOUT HYPOTHESIS TESTING A measure of effect size is intended to provide
 a measurement of the absolute magnitude
 of a treatment effect, independent of
 the size of the sample(s) being used. 29 MEASURING EFFECT SIZE (Gravetter & Wallnau, 2010, p. 262) z = Mtreatment - µno treatment !
  33. 33. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati CONCERNS ABOUT HYPOTHESIS TESTING 30 MEASURING EFFECT SIZE µ = 32 ! = 10 µ = 32 ! = 10 (Gravetter & Wallnau, 2010, p. 262-264)
  34. 34. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati CONCERNS ABOUT HYPOTHESIS TESTING 30 MEASURING EFFECT SIZE µ = 32 ! = 10 µ = 32 ! = 10 (Gravetter & Wallnau, 2010, p. 262-264)
  35. 35. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati CONCERNS ABOUT HYPOTHESIS TESTING 30 MEASURING EFFECT SIZE µ = 32 ! = 10 d = 0,15 µ = 32 ! = 10 d = 1,00 d = 0,20 SMALL EFFECT (mean difference around 0,2 standard deviation) d = 0,50 MEDIUM EFFECT (mean difference around 0,5 standard deviation) d = 0,80 LARGE EFFECT (mean difference around 0,8 standard deviation) (Gravetter & Wallnau, 2010, p. 262-264)
  36. 36. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati CONCERNS ABOUT HYPOTHESIS TESTING The power of a statistical test is the probability
 that the test will correctly reject a false null hypothesis.
 That is, power is the probability that the test will identify
 a treatment effect if one really exists. 31 STATISTICAL POWER
  37. 37. FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA PDU 207 STATISTIK DASAR© 2015 Ardhiati CONCERNS ABOUT HYPOTHESIS TESTING The power of a statistical test is the probability
 that the test will correctly reject a false null hypothesis.
 That is, power is the probability that the test will identify
 a treatment effect if one really exists. 31 STATISTICAL POWER 32 !M = 10 !M = 10 4222 5212 7262 82 92 Reject
 H0 Reject
 H0 0 +1,96-1,96 z
  38. 38. WANT TO KNOW MORE? GRAVETTER, F.J. & WALLNAU, L.B. (2012). STATISTICS FOR THE BEHAVIORAL SCIENCES (9TH ED.). AUSTRALIA: WADSWORTH CENGAGE LEARNING.

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