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Psychology

PSYC 203

Shana Clifford

Spring

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PSYC 203 Exam 2 Review
Probability and the Normal Curve (Chapter 8)
Attributes of the Normal Curve
• The normal or bell-shaped curve (with a large enough sample size)
• 3 defining features
o mean, median, and mode are equivalent
o perfectly symmetrical
o asymptotic (tails get closer and closer to the x-axis but never touch it): there is always some
probability of an extreme score; the probability gets smaller the further you move away from the
mean; extreme values are unlikely
Probability and the Normal Curve
• Randomly picking a person from the population, the odds that they are “average” height is higher than
the odds that they are very short or very tall
o Reason: there are more of them
• The normal curve is split into sections by standard deviations
• Almost all values will fall between -3 and +3 standard deviations from the mean
• Normal curve probability allows us to determine the likelihood of getting a score bigger/smaller than
any single score
Z-Scores
• To identify and describe the exact location of a score in its “home” distribution; transform a raw score to
be directly compared across distributions
• Z-scores tell you how far a point is from its mean by means of standard deviation units
• Z-scores tell you the probability of getting a score higher/lower than that score
• The %’s represents the probability that a score would occur in the range you’ve defined
• Percentile Rank- a score that indicates the percentage of people who scores at or below a given raw
score
Null Hypothesis Significance Testing (Chapter 9)
• When we observe events that are very unlikely (i.e less than 5% probability of occurring) under the null,
we reject it
• In NHST, we calculate the probability (p-value) of obtaining our data IF the null hypothesis was TRUE
• P-values are widely reported in journal articles
Four Stages of NHST
• Stage 1: state the hypothesis
o Compare quiz scores of students who study listening to instrumental music vs. Norwegian death
metal
• Stage 2: set significance level (alpha)
o Set at .05 • Stage 3: compute statistics
o Mean and SD
• Stage 4: make a decision…REJECT or FAIL TO REJECT the null?
o If p-value is lower than .05 – reject the null
o If p-value is higher than .05 – fail to reject the null
Type I and Type II Errors
• Type I error: false positive (telling a man he is pregnant)
o Can reduce Type I errors by setting alpha lower (like .001) but will increase risk of Type II error
• Type II error: false negative (telling a pregnant woman she’s not pregnant)
o Causes: sampling error, measurement error, small sample sizes (low power)
o Consequences: missing out, truth may never be uncovered
One Sample Z-Test (Chapter 10)
Appropriate Use
• Use when we want to test the difference between a sample mean and the population mean (inferential
test)
• You need: population mean and SD, sample mean and sample size (n)
Famous 8 Steps
1. State the hypothesis
2. Set the significance level (alpha at .05) that will cause you to reject the NULL hypothesis
3. Select the appropriate inferential test statistic
4. Use the selected inferential test to compute a test statistic (used to compute p-values)
5. Determine the CRITICAL VALUE (1.96 and -1.96 for p < .05 with two-tailed test) for the test statistic -
the minimum value needed to reject the null hypothesis
6. Compare your obtained test statistic to the critical value
7. Make a decision – reject the null if your obtained value is bigger than the critical value; fail to reject
(retain) the null if the obtained value is smaller than the critical value
The Standard Error of the Mean
• Difference or “error” between sample means and mu
• The SEM is the standard deviation of sample means – the typical distance between M and mu
• The means are typically closer to the population value for larger samples than smaller samples
• The larger the test statistic, the smaller the p-value
H0 is true (no difference exists between groups) + reject H0 (p < .05) = Type I error (false positive)
H0 is false (there really is a difference between groups) + fail to reject H0 (p > .05) = Type II error (false
negative)
Independent Samples t-test (Chapter 11 and Lab 5)
Appropriate Use
• Use when we want to test the difference between samples means from two separate groups (widely
used) …assumes homogeneity of variance
o Ex:

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