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Final

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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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