Download Review of Assumptions

Assumptions for Procedures
Testing One Population Mean
• Use a t-test or interval if
– Sample is a valid SRS from the population of
interest
– Population is approximately normal
• Sample size < 15 needs approx. normal
– Check by graphing data
• Sample size > 15 can accept some skewness or
non-extreme outliers
– Check by graphing data
• Sample size > 30 can accept any population
distribution by Central Limit Theorem
– Don’t need to graph, but assert C.L.T.
Comparing Two Population Means
• Two SRS’s from distinct populations
• Both populations are normally distributed
– Same sample size restrictions as one-pop
• Samples are independent
• Both samples measure the same variable
Matched-Pairs vs. Two-Pop
• Matched Pairs test
– Only one group of subjects is measured
– Each subject is measured twice
– It makes sense to subtract individual scores
– Perform test on the mean of individual differences
• Two-Population test
– Two different groups of subjects are measured
– Perform test on the difference of group means
Testing One Population Proportion
• Data are an SRS from the population
• Population size is at least ten times
sample size
• Sample size is large enough that both the
expected “yes” and “no” counts are 10 or
more
np  10
n(1  p )  10
Comparing Two Population
Proportions
• Data are an SRS from the population
• Population size is at least ten times
sample size
• Sample size is large enough that both the
expected “yes” and “no” counts are 5 or
np  5
more
n(1  p)  5
• Can use either a 2-PropZTest or X2 Test
X2 Goodness of Fit Test
• All expected counts are at least 1
• No more than 20% of the expected counts
are less than 5
• Check expected counts in matrix B after
running test
Linear Regression Slope Test
• Use to establish association between two
numeric variables
• Assumptions
– The true relationship is linear
• So a scatterplot of sample data should appear linear
• The residual plot should be a patternless cloud of points
– The response varies normally about the regression
line
• A normal probability plot of the residuals should look linear
– The standard deviation of the response about the true
line is the same for all x values
• The residual plot should have a uniform width across the full
range of x values