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PSYC512: Research Methods Lecture 9PowerPoint Presentation

PSYC512: Research Methods Lecture 9

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Lecture 8 Outline

- Exam Next Week
- Will cover all lecture material, all material in Howell Chapters 1-5, broad concepts assumptions from Howell Chapters 6-11
- What do I mean by “broad concepts?”
- which tests are associated with which types of scaling properties of variables?
- What variants of the tests exist and why?
- What assumptions underlie the test?

- Questions about material covered in Lecture 8
- Describing Data

- The Normal Distribution
- Testing Hypotheses
- Inferential Statistics

PSYC512: Research Methods

Review: The Normal Distribution

- What is the difference between a normal distribution and a standard normal distribution?
- What is the difference between a raw score and a standardized score?
- What are confidence intervals?

PSYC512: Research Methods

Testing Hypotheses

- Hypothesis testing is the process by which hypothetical relationships between intervening variables are assessed
- Hypotheses are always tested relative to one-another or to a “null” hypothesis
- Examples
- Comparing groups
- Assessing performance interventions
- Assessing relationships between variables

PSYC512: Research Methods

Null-Hypothesis Testing and Inferential Statistics

- 2 possible realities
- Relationship between your variables does not exist—a null relationship (Ho, the null hypothesis)
- Relationship between the two variables in question actually exists (H1, the experimental or alternative hypothesis)

- 2 possible decisions when looking at the data
- Conclude that a relationship exists (reject the null hypothesis, Ho DISCONFIRMATION!)
- Conclude that no relationship exists (do not reject the null hypothesis CONFIRMATION? NO!)

PSYC512: Research Methods

Null-Hypothesis Testing and Inferential Statistics

True State of the World

2 realities by 2 decisions form a 2 x 2 matrix of 4 possibilites

Decision

PSYC512: Research Methods

Null-Hypothesis Testing and Inferential Statistics

1 Population

- Why might we observe a difference between two groups if no difference actually exists (null is true; samples are drawn from the same population)?
- Each sample may have a unique mean due to sampling error

Frequency

m

2 samples

Frequency

PSYC512: Research Methods

Null-Hypothesis Testing and Inferential Statistics

2 Populations

- How does this change if a difference actually exists between my groups?
- Each sample has a unique mean that represents both sampling error and the differences between the 2 populations

Frequency

m1

m2

Frequency

PSYC512: Research Methods

Hypothesis Testing: Probability and Statistics

- Problem: How do we distinguish real differences or relationships from measurement noise?
- Probability and statistics may be used to assess (descriptive statistics) or compare (inferential statistics) the relative magnitude of different types of variability
- Effect (treatment) Variance
- Variability due to relationship between variables or effect of different levels of independent variable (treatments)
- “Good” variance that we want to maximize

- Error Variance
- Variability in measure due to factors other than the treatment
- “Bad” variance that we want to minimize

- Effect (treatment) Variance

PSYC512: Research Methods

Hypothesis Testing: Inferential Statistics

- All inferential statistics are evaluating this ratio:
Effect (good) Variance

Test statistic = --------------------------------------

Error (bad) Variance

- Example test statistics: Chi-square, t, F
- These test statistics have known distributions that then allow us to estimate p, the probability of a Type I error (inappropriately rejecting the null hypothesis)
- Decision to reject null is made by comparing p to some generally accepted criterion for Type I error probability, a = .05

PSYC512: Research Methods

How is the probability of a Type I error, p, calculated? It depends on…

- Scaling properties of your dependent variable (DV)
- DV is interval or ratio parametric tests
- DV is nominal or ordinal non-parametric tests

- Research design
- Experimental – test differences on measure between conditions or groups t-test, ANOVA, sign test, Mann-Whitney
- Correlational – test relations between different measures Pearson product-moment correlation, point-biserial correlation, etc.

- Manner in which you phrase your hypotheses
- One tailed vs. two-tailed tests

PSYC512: Research Methods

Examples?

PSYC512: Research Methods

Next Time…

- Topic: Review of broad concepts related to power, Chi-square, t-tests, and correlation
- Be sure to:
- Review Howell chapters 6-10
- Bring questions!
- Continue searching and reading the scientific literature for your proposal

PSYC512: Research Methods

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