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Final

Final Exam Review P1.doc

4 Pages
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Department
Psychology
Course Code
PSYC 305
Professor
Heungsun Hwang

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Description
PSYC305 Final Exam Review Week 1: Basic Statistics • Population: The entire set of things of interest • Parameter: A property descriptive of the population • Sample: The part of the population. Typically this provides the data we will look at • Estimate: A property of a sample • Descriptive Statistic: Summarize/describe the properties of samples (or populations when they are completely known) • Inferential Statistic: Draw conclusions/make inferences about the properties of populations from sample data • Types of Variables: • Nominal - cannot be ranked, non numeric, categorical (discrete/qualitative) • Ordinal - can be ranked, non numeric, categorical (discrete/qualitative) • Ratio - ranked, numeric, true zero, numerical (continuous/quantitative) • Interval - ranked, numeric, no true zero, numerical (continuous/quantitative) • DV - Continuous (normally distributed) • IVs - Categorical/continuous • Mean: Average; balancing point. Affected by extreme values Median: Exact middle value; not affected by extreme values • • Mode: Value that occurs most frequently; not affect by extremely values. Used for either numerical or categorical data • Range: Measure of dispersion. Difference between the largest and the smallest observations • Variance: Average (approximately) of ‘squared’ deviations of values from the mean • Standard Deviation: Shows variation about the mean. Has the same units as the original data • The dependent variable (Y) is assumed to be continuous and normally distributed • If normally distributed, • Mean = Median = Mode • Mean and Standard Deviation are sufficient to describe a normal distribution • µ ± 1ơ = 68% of values in population or sample • µ ± 2ơ = 95% of values in population or sample µ ± 3ơ = 99.7% of values in population or sample • Week 2: Hypothesis Testing - Comparing One/Two Means • Steps for Hypothesis Testing: 1. Set up a hypothesis • Null Hypothesis • No effect • Alternative hypothesis: research/experimental hypothesis • Some hypothesis 2. Decide significant level • a = .05 3. Examine empirical data and compute the appropriate test statistic 4. Make the decision whether to ‘reject’ or ‘not reject’ the null hypothesis • Compare the calculated value of your test statistic to the (tabled) critical value for a • If your value is greater than the critical value, reject null hypothesis • Otherwise, accept null hypothesis • Alternatively, look at the significance level (p-value) of your test statistic value If p-value < .05, reject null hypothesis • • If null hypothesis is rejected, you may conclude that there is a statistically significant effect in the popula- tion • Effect Size: An objective and standardized measure of the magnitude of a treatment effect • Commonly used measures of effect size: • Pearson’s correlation coefficient (r) - used for z-tests, t-tests • Omega - used for all ANOVAs • Cohen’s d • Cohen (1988): • R = .10 (small effect) • R = .30 (medium effect) R = .50 (large effect) • • Z-test: • Purpose: To test whether a sample mean significantly differs from a population mean H : µ = 100 • 0 • H 1 µ ≠ 100 • Prior Requirements/Assumptions: The population is normally distributed • • The mean and standard deviation of the population must be known The sample must be a simple random sample of the population • • Methods: The z-test for a single mean is equivalent to calculating the z score of your sample mean • • Convert our sample score (X) to a standard score (z) which follows the standard normal distribution • Look into how extreme your sample mean is based on its z-score • If this z-score in absolute value is larger than 1.96, you may reject the null hypothesis • Limitations of z-test: • Knowing the true value of the standard deviation of a population is unrealistic • T-test (Single Mean): • Purpose: To test whether a sample mean significantly differs from a population mean • H 0 µ = 100 • H 1 µ ≠ 100 • Prior Requirements/Assumptions: • The population is normally distributed • The mean of the population must be known • The sample must be a simple random sample of the population • Methods: • T-statistics is obtained by replacing the standard deviation of the population mean with the sample counterpart in z -statistics • Due to this replacement, t-statistic does not follow the standard normal distribution anymore. Instead, it follows the t-distribution • Also called Student’s t-distribution • Varies in shape according to degrees of freedom (DF) = N-1 • The t-distribution approaches the standard normal distribution as DF becomes large (roughly 30) • Calculate et value of t-statistic (or simply t-value) for your sample mean • Look into how extreme your t-value is and compare to critical value from t-distribution chart • If your t-value in absolute value is larger than the critical value, you may reject the null hypothesis • Alternatively, look at the p-value; if p < .05, you may reject null hypothesis • T-test (Two Means): • Purpose: To test whether two unknown population means are different from each other based on their samples. The two samples may be either independent or correlated • H 0 µ 1 µ 2 • H 1 µ 1 µ 2 • Independent Samples: Where two different groups of subjects are used for two separate treatment • Correlated Samples (One-Way ANOVA Repeated Measures): Where the same group of subjects are used for the two separate treatment • Prior Requirements/Assumptions: • Both populations are normally distributed • The standard deviations of the populations are the same Homogeneity of variance (ơ = ơ1) 2 • • Each sample must be a simple random sample of the population • Methods: • The t-statistic for two independent samples is virtually of the same form as that for a single mean • Calculate et value of t-statistic (or simply t-value) for your sample mean • Look into how extreme your t-value is and compare to critical value from t-distribution chart If your t-value in absolute value is larger than the critical value, you may reject the null hypothesis • • Alternatively, look at the p-value; if p < .05, you may reject null hypothesis Week 3: One-Way ANOVA I • Independent variable (IV): Called a factor
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