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15 Cards in this Set
- Front
- Back
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What is the estimated standard error? |
(sm) is used as an estimate of the real standard error (sigma subscript m) when the value of standard deviation is unknown. It is computed from the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean, M, and the population mean, Mew |
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t-statistic |
is used to test hypothesis about an unknown population mean, mew, when the value of standard deviation is unknown. The formula for the t statistic has the same structure as the z-score formula, except that the t statistic uses the estimated standard error in the denominator. |
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Degrees of freedom |
describe the number of scores in a sample that are independent and free to vary. Because the sample mean places a restriction on the value of one score in the sample, there are n-1 degrees of freedom for a sample with n scores. |
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A t distribution |
is a complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df). The t distribution approximates the shape of a normal distribution. |
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What is the difference between a t distribution and a normal z-score distribution? |
t distributions have more variability, indicated by the flatter and more spread-out shape. The larger the value of df is, the more closely the t distribution approximates a normal distribution. |
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Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? |
A t statistic is used instead of a z-score when the population standard deviation and variance are not known. |
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What are 2 assumptions of the t test? |
1. The values in the sample must consist of independent observations. 2. The population that is sampled must be normal. |
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What is the effect of a larger value for Sm in the t formula? |
This produces a smaller value for t. |
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The two factors that determine the size of the standard error are: |
Sample variance (s^2) and sample size (n). |
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For standard error, the larger the variance, what happens to the error? |
It increases. You are less likely to obtain a treatment effect. High variance reduces the likelyhood of rejecting the null hypothesis. |
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What effect does a larger sample size have on error in a t test? |
Larger sample size = smaller error. |
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What criteria is recommended for interpreting the value of r^2 as proposed by Cohen? |
r^2=0.01 small effect r^2=0.09 Medium effect r^2=0.25 Large effect |
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What two characteristics of the confidence interval are considered? |
1. To gain more confidence in your estimate, increase the width of the interval. It gain more precision, decrease the interval and reduce confidence. 2. The bigger the sample (n), the smaller the interval. As the sample size increases, the standard error decreases, and the interval gets smaller. |
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How does sample size influence the outcome of a hypothesis test and measures of effect size? |
Increasing sample size increases the likelihood of rejecting the null hypothesis but has little or no effect on the measures of effect size. |
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How does the standard deviation influence the outcome of a hypothesis test and measures of effect size? |
Increasing the sample variance reduces the likelihood of rejecting the null hypothesis and reduces measures of effect size. |
