Psych 311 Unit 9 Study Guide
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1
Parametric tests
- Require assumptions about population parameters
- Require numerical scores
- Can be used to calculate mean & standard deviation
- Use ratio & interval data
- Testing hypotheses: Use population parameters
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Nonparametric tests
- DO NOT require assumptions about population parameters
- DO NOT require numerical scores; use categories, names, and groupings'
- CANNOT be used to calculate mean & standard deviation
- Use nominal and ordinal data
- Testing hypotheses: DO NOT state specific, numeric, population parameters
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When to use nonparametric tests
- When Simplicity is Needed
- Sometimes categories are simpler than scores (and still useful)
- When
scores violate assumptions of parametric tests
- For instance, parametric tests require normal distributions
- When variance is extremely high
- Extreme variance makes statistical significance unlikely
- Categories allow diverse scores to fit (ex. High, Medium, Low)
- With Indeterminate or Infinite Scores
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Research Designs for T Tests
- Single Sample
- Uses a single sample to make inferences about a single population
- Two Unrelated Samples
- Uses two samples to make inferences between two unknown populations
- Two Related Samples
- Uses one sample with each individual tested in two treatment conditions to make inferences about mean population differences
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T Test: Hypothesis testing
- GOAL: Use sample from treated population (treated sample) to
determine whether treatment has effect.
- Population mean is UNKNOWN
- Sample Mean is KNOWN, as is estimated standard error
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T Test: Null hypothesis
- Null hypothesis states that there is no treatment effect and that the population mean is unchanged
- Null hypothesis provides a specific value for the unknown population mean
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T Test: Reporting

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T Test: Types
- Single Sample
- Uses sample data (one sample) to test a population mean
- Independent Samples
- Uses data from two separate samples to evaluate mean difference between two different treatment conditions or populations
- Two sets of data
- Completely separate (independent) groups of participants
- Repeated Measures Designs
- Uses two sets of data from the same sample of participants to evaluate mean difference
- Two sets of data
- The same group of participants
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T Test: Types (reporting differences)
-
Independent
Samples:
- Since it involves two separate samples, extra notation is needed
- Subscripts are used, with number indicating which sample (1 or 2)
- n 1, n 2 (sample size); M 1, M 2 (means), SS 1, SS 2 (sum of squares; μ 1 - μ 2 (population mean difference)
-
Repeated Measures
Designs
- Uses sample mean difference (M D) to estimate population mean difference (μ D)
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Independent Samples: Advantages and Disadvantages
-
Pro’s:
- No potential for order effects
- No potential for time-related factors
-
Con’s:
- Less efficient (more participants needed)
- Less ideal for studying changes over time
- Potential problems with individual differences
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Repeated measures: Advantages and Disadvantages
-
Pro’s:
- More efficient (fewer participants needed)
- Good for studying changes over time
- Reduces problems caused by individual differences
-
Con’s:
- Potential for order effects
- Potential for time-related factors
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T Test Vs. ANOVA
- T-test: can only compare two treatments
- ANOVA: can compare 2 or more treatments
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ANOVA
- Definition
- Analysis of Variance
- It is a hypothesis testing procedure used to evaluate mean differences between two or more populations or treatments
- Uses sample data to make inferences about populations
- FACTOR
- The variable (independent or quasi-independent) that designates the groups being compared
- LEVELS
- Individual conditions or values that make up a factor
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Types of ANOVA Designs
- Single-Factor
- Studies that have one independent variable (one factor)
- Independent-Measures
- Separate group of participants for each treatment being compared
- Repeated-Measures
- Same group of participants is tested in all treatment conditions
- Two-Factor
- Studies that have two independent variables (two factors)
- Can address different questions than single-factor designs
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Null Hypothesis for ANOVA
- States that there is no treatment effect and that the population mean is unchanged
- Provides a specific value for the unknown population mean
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Types of ALPHA
- Testwise Alpha
- The risk of a Type I error, or alpha level, for an individual hypothesis test
- This is what we’ve talked about for the whole semester
- Experimentwise Alpha
- Is the total probability of a Type I error that accumulates when several hypothesis tests are used in a single study
- Typically larger than testwise alpha
- Is the reason why multiple t-tests should be run to compare three groups (use ANOVA instead)
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Reporting ANOVA

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Post-Hoc Tests
- What are they?
- Additional hypothesis tests that are run after an ANOVA to determine exactly which mean differences are significant and which are not
- When to use them?
- When you have a significant F statistic and there are more than two groups
- F-statistic does not indicate where the significance is
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Chi-Square Test for Goodness of Fit
- Uses sample data to test hypotheses about the shape or proportion of a population distribution
- Determines how well sample proportions fit population proportions of null hypothesis
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Chi-Square Test for Goodness of Fit: Data Presentation

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Types of null hypotheses for Chi-Square

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Types of null hypotheses for Chi-Square

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Correlational Research Strategy
- Two or more variables are measured to obtain a set of scores (usually 2) for each individual (or source)
- Measurements are examined to identify patterns that exist between the variables and to measure the strength of the relationship
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What correlations describe
- The direction of the relationship
- Positive or negative relationships
- The form of relationship
- Linear (using Pearson correlation)
- Monotonic (using Spearman correlation)
- The consistency or
strength of relationship
- How close the relationship is to a perfect linear or a perfect monotone relationship
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Correlational Vs. Experimental
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Correlational
- Goal: Demonstrating the existence of a relationship between variables (not explaining)
- NO manipulating or controlling variables
- Measures two different variables
-
Experimental
- Goal: Demonstrating cause and effect, explaining relationship between variables
- DOES manipulate and control certain variables
- Usually only one measured (dependent) variable and looks for differences between two or more groups of scores