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Questions and Answers
What does the standard error of the mean, denoted as σₘ, primarily indicate?
What does the standard error of the mean, denoted as σₘ, primarily indicate?
- The probability of rejecting the null hypothesis when it is true.
- The exact difference between a sample mean (M) and the population mean (𝛍).
- The average expected difference between sample means (M) and the population mean (𝛍). (correct)
- The variability of individual scores within a sample.
According to the law of large numbers, what happens as the sample size increases?
According to the law of large numbers, what happens as the sample size increases?
- The need for hypothesis testing diminishes.
- The sample mean (M) becomes less likely to accurately represent the population mean (𝝁).
- The probability that the sample mean (M) is close to the population mean (𝝁) increases. (correct)
- The standard deviation of the sample increases proportionally.
In hypothesis testing, what defines the critical region?
In hypothesis testing, what defines the critical region?
- Outcomes that are very unlikely to occur if the null hypothesis is true. (correct)
- Outcomes that are highly likely to occur if the null hypothesis is true.
- Outcomes that support the null hypothesis.
- Outcomes with exactly a 50% chance of occurring.
If a z-score calculated from a sample is +/- 2.5, what decision should be made regarding the null hypothesis, assuming ɑ=0.05?
If a z-score calculated from a sample is +/- 2.5, what decision should be made regarding the null hypothesis, assuming ɑ=0.05?
What does Cohen’s d measure?
What does Cohen’s d measure?
When is it most appropriate to use a t-test instead of a z-test?
When is it most appropriate to use a t-test instead of a z-test?
In a one-sample t-test, what does the denominator of the t-statistic, sm, represent?
In a one-sample t-test, what does the denominator of the t-statistic, sm, represent?
What information does $r^2$ provide in the context of a t-test?
What information does $r^2$ provide in the context of a t-test?
In an independent-measures t-test, what is assumed about the populations being compared?
In an independent-measures t-test, what is assumed about the populations being compared?
What does the denominator, S(M1-M2), in the formula for the independent samples t-test represent?
What does the denominator, S(M1-M2), in the formula for the independent samples t-test represent?
Flashcards
Standard Error of the Mean
Standard Error of the Mean
The standard deviation of the distribution of sample means; measures the average difference between a sample mean (M) and the population mean (μ).
Law of Large Numbers
Law of Large Numbers
The principle stating that as the sample size increases, the sample mean (M) is more likely to be close to the population mean (μ).
Critical Region
Critical Region
A region of outcomes that are very unlikely to occur if the null hypothesis is true, typically defined by a significance level (α) of 0.05.
P-value
P-value
The probability of obtaining an effect at least as extreme as the one in your sample data, assuming the null hypothesis is true.
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Effect Size
Effect Size
A measure of the absolute magnitude of an effect, independent of sample size.
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Cohen’s d
Cohen’s d
A standardized measure of effect size that expresses the mean difference in terms of the standard deviation.
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T-test
T-test
A hypothesis test used when the population standard deviation is unknown; it estimates the standard error using the sample standard deviation.
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One Sample T-test
One Sample T-test
A type of t-test used to test hypotheses about a population mean when the population standard deviation is unknown.
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r²
r²
The percentage of variance in the dependent variable that is accounted for by the independent variable.
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Independent Samples T-test
Independent Samples T-test
A type of t-test used to evaluate the mean difference between two unknown populations using data from two independent samples.
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- σₘ= σ/√n represents the standard error.
- Standard error of the mean measures the average expected difference between M and 𝛍.
- It describes the distribution of sample means (variability).
- Less spread in distribution means it is unusual to get something far from the mean; more spread means it is less unusual.
- Law of large numbers states the larger the sample size, the more probable that M is close to 𝝁.
- z= (M-𝝁)/σₘ is the z-score formula.
- Critical region consists of outcomes very unlikely to occur if the null hypothesis is true.
- Defined by associations that are very unlikely if no effect exists (less than 5% chance if ɑ=0.05).
- Z-scores of +/- 1.96 define the critical region; reject the null hypothesis if z-score falls within this region.
- P-value is the probability of obtaining an effect at least as extreme as the one in your sample data, assuming the null hypothesis is true.
- Effect size measures the absolute magnitude of an effect independent of sample size.
- Hypothesis tests should be accompanied by effect size measures.
- Cohen’s d is a standardized effect size that measures mean difference in terms of standard deviation.
- Cohen’s d formula: M-𝝁/σ
T-Tests
- T-statistic does not require knowledge of the population standard deviation (σ).
- T-tests can test hypotheses for a completely unknown population, which occurs when both 𝝁 and 𝞂 are unknown.
- One sample t-test is similar to a z-test but used when population standard deviation is unknown.
- Independent samples or independent measures t-tests are used.
- t-tests formula: sm=s/√n
- t=(M-𝝁)/sm, where the numerator is the difference between the sample mean and hypothesized population mean, and the denominator is the estimated standard error.
- r2= percentage of variance accounted for by the IV. Used as new measure of effect size
- r2= t2/t2+df
Independent Sample T-Tests
- Independent measure designs evaluate the mean difference between two unknown populations using data from two samples.
- Both population means and standard deviations are unknown and must be estimated from the sample data.
- Non directional hypothesis: H0: 𝝁1=𝝁2 and HA: 𝝁1=/𝝁2
- Directional hypothesis: H0:𝝁1>𝝁2 and HA: 𝝁1
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