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t-Statistic - measures the size of the difference between your sample data…
t-Statistic - measures the size of the difference between your sample data and what you would expect to find under the null hypothesis, relative to the variation in your data.
Estimated Standard Error (sM) - used as an estimate of the actual standard error (σM), when the value of σ 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 μ.
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the sample variance (s squared) provides an accurate and unbiased estimate of the population variance (σ squared).
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Used to test hypotheses of unknown population mean (μ), when the value of s 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.
Only difference between the t formula and the z-score formula is that the z-score uses the actual population variance (σ squared), (or the standard deviation), and the t formula uses the corresponding sample variance (or standard deviation) when the population value is not known.
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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You can compute the t statistic for every sample and the entire set of t values will form a t distribution.
A t distribution is the 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.
Hypothesis Testing
t = sample mean (from data) - population mean (hypothesized from null hypothesis) / estimated standard error (computed from the sample data).
The estimated standard error is directly related to the sample variance so that the larger the variance, the larger the error.
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Cohen (d) defined this measure of effect size in terms of the population mean difference and the population standard deviation.
Estimated d - researchers use this in most situations the population values are not known and you must substitute the corresponding sample values in their place.
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An alternative method for measuring effect size is to determine how much of the variability in the scores is explained by the treatment effect.
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Confidence Interval - an interval, or range of values centered around a sample statistic. The logic behind a confidence interval is that a sample statistic, such as a sample mean, should be relatively near to the corresponding population parameter. Therefore, we can confidently estimate that the value of the parameter should be located in the interval near to the statistic.
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To gain more confidence in your estimate, you must increase the width of the interval.
To have a smaller, more precise interval, you must give up confidence.
The bigger the sample (n), the smaller the interval
1 or 2 Tail Test
Step 1:State the Hypotheses, and Select an Alpha Level. Step 2: Locate the Critical Region. Step 3: Calculate the Test Statistic. 4: Make a Decision.
