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Chapter 9: Introduction to the t Statistic, Hypothesis with t-statistic;…
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Hypothesis with t-statistic; goal is to use a sample from the treated population (a treated sample) as the basis for determining whether the treatment has any effect.
Null hypothesis states that the treatment has no effect - null hypothesis provides a specific value for the unknown population mean. t= sample mean (from the data) - population mean (hypothesized from null hypothesis)/estimated standard error (computed from the sample data)
t-statistic can be used in the "before & after" type of research, it also permits hypothesis testing in situations for which you do not have a known population mean to serve as a standard.
- State the hypothesis and select an alpha level.
- Locate the critical region (df) = n-1
- Calculate the statistic s^2 = SS/n-1 = SS/df
- Make decision regarding Null Hypothesis.
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Measuring the Percentage of Variance Explained, r^2
determine how much of the variability in the scores is explained by the treatment effect: concept is that the treatment causes the scores to increase (or decrease), which means that the treatment is causing the scores to vary.
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To measure how much variability is reduced when the treatment effect is removed, we compute the sum of squared deviations, SS, for each set of scores.
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Confidence Intervals for Estimating mean (m) - is 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.
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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.
- If you change the sample size: the bigger the sample (n), the smaller the interval.
Estimated Cohen's d (name the value after one of the statisticians who first submitted sample statistics into Cohen's formula) - in most situations the population values are not known and you must substitute the corresponding sample values in their place
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Critical Region for a One-Tailed Test - 1. determine whether the sample mean is in the direction predicted by the original research question. 2. Determine whether the effect is large enough to be significant.
