Samples drawn so that no member of one sample is linked to any member of the other are called independent, as opposed to dependent or paired samples.
Missing Word
independent
Independent samples are selected separately, so knowing who is in one group says nothing about who is in the other. Different methods are needed when the samples are linked, as in matched pairs.
Category: Choosing the Test
Question 2
A two-sample z test for a difference in means can be used only when both population standard deviations are known.
Missing Word
known
Known here means the values of sigma1 and sigma2 are available before the data are analyzed. When they must be estimated from the samples, the t distribution replaces z.
Category: Comparing Two Means
Question 3
In a matched pairs test, the data analyzed are the differences between the two measurements in each pair.
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differences
The differences turn two linked sets of measurements into one sample. Their mean and standard deviation are then used in a one-sample t test.
Category: Matched Pairs
Question 4
When forming the data for a matched pairs test, every difference must be computed with the same order of subtraction, for example after minus before.
Missing Word
subtraction
Subtraction in a consistent order, such as after minus before, gives every difference the same meaning. Mixing orders would scramble the signs and hide any real effect.
Category: Matched Pairs
Question 5
In a matched pairs test of whether a treatment has any effect, the null hypothesis states that mu_d equals zero.
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zero
Zero is the hypothesized population mean difference when the treatment has no effect, so H0: mu_d = 0. The alternative then says mu_d is greater than, less than, or not equal to 0.
Category: Matched Pairs
Question 6
In the two-sample t statistic, the observed difference x-bar1 - x-bar2 minus its hypothesized value forms the numerator.
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numerator
The numerator is the top of the fraction: how far the observed difference is from what H0 claims. The standard error in the bottom of the fraction scales that distance.
Category: Comparing Two Means
Question 7
The effect size d, found by dividing the difference between two sample means by their pooled standard deviation, is named for the psychologist and statistician Jacob Cohen.
Missing Word
Cohen
Cohen's d expresses the gap between two group means in standard deviation units, so it does not depend on the original units of measurement. Jacob Cohen also proposed the familiar benchmarks of about 0.2, 0.5 and 0.8 for small, medium and large effects.
Category: Effect Size
Question 8
The Aspin-Welch t test does not pool the two sample variances, since it does not require the population standard deviations to be equal.
Missing Word
variances
Variances are squared standard deviations. Keeping them separate in the standard error lets the test handle populations with different spreads.
Category: Comparing Two Means
Question 9
By the usual benchmarks for d, an effect size of 0.8 is considered large.
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large
The standard benchmarks for Cohen's d are about 0.2 for small, 0.5 for medium and 0.8 for large effects. A large effect means the group means differ by roughly eight tenths of a standard deviation or more.
Category: Effect Size
Question 10
With small samples, the two-sample t test requires each population to be approximately normal.
Missing Word
normal
A normal population has a bell-shaped distribution. With small samples the t test relies on this; with large samples the sampling distribution of the difference in means is close to normal regardless.
Category: Comparing Two Means
Question 11
A two-sample z test that combines the counts from both groups into one pooled estimate compares two population proportions.
Missing Word
proportions
Proportions are the fractions of each population with a trait. When H0 says they are equal, the data from both groups are combined to estimate the shared value.
Category: Comparing Two Proportions
Question 12
When each pair is scored as after minus before, a negative mean difference shows that scores fell on average.
Missing Word
negative
A negative difference means the after value was smaller than the before value. The sign of the mean difference therefore tells the direction of the change.
Category: Matched Pairs
Question 13
Both samples in a two-sample test should be random, so that every member of each population has an equal chance to be chosen.
Missing Word
random
Random selection protects against bias and is what allows the sample results to be generalized to the populations. The probability calculations in the test depend on it.
Category: Choosing the Test
Question 14
For a two-proportion z test, each sample should contain enough successes and failures for the z test to be reliable.
Missing Word
successes
A success is an outcome with the trait being counted. With enough successes and failures in each sample, the difference in sample proportions is approximately normal.
Category: Comparing Two Proportions
Question 15
A study that gives the two members of each pair of identical twins different treatments is a classic example of a matched pairs design.
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twins
Identical twins share genes and usually upbringing, so comparing one twin with the other removes much of the natural variation between people. Each set of twins forms one pair, and the analysis uses the difference within each pair.
Category: Matched Pairs