Statistics For Dummies, 2nd Edition (For Dummies (Lifestyle))

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Confounding variables are ones that were not included in a study but can influence the results. They are a major source of bias. When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. Hypothesis tests are used to test the validity of a claim that is made about a population. This claim that’s on trial, in essence, is called the null hypothesis. Your 95 percent confidence interval for the mean length of walleye fingerlings in this fish hatchery pond is 7.5 inches ± 0.45 inches.

Because the z-table gives you only "less than" probabilities, find the difference between the probability less than 1.0 and the probability less than –0.5:

For example, suppose a pizza place claims their delivery times are 30 minutes or less on average but you think it’s more than that. You conduct a hypothesis test because you believe the null hypothesis, H o, that the mean delivery time is 30 minutes max, is incorrect. Your alternative hypothesis (H a) is that the mean time is greater than 30 minutes. Upfront and honest answers to your questions like, “What does this really mean?” and “When and how I will ever use this?”

Understanding how to get a p-value from a test statistic is essential for assessing whether the results of your test are likely to have occurred by chance, assuming the null hypothesis is true. However, this may lead you to wonder whether it’s okay to say “Accept Ho” instead of “Fail to reject Ho.” The answer is a big no. As mentioned above, in statistics, r values represent correlations between two numerical variables. The value of r is always between +1 and –1. To interpret r value (its meaning in statistics), see which of the following values your correlation r is closest to: You can find a confidence interval (CI) for the difference between the means, or averages, of two population samples, even if the population standard deviations are unknown and/or the sample sizes are small. The goal of many statistical surveys and studies is to compare two populations, such as men versus women, low versus high income families, and Republicans versus Democrats. When the characteristic being compared is numerical (for example, height, weight, or income), the object of interest is the amount of difference in the means (averages) for the two populations. When designing a study, the sample size is an important consideration because the larger the sample size, the more data you have, and the more precise your results will be (assuming high-quality data). If you know the level of precision you want (that is, your desired margin of error), you can calculate the sample size needed to achieve it.

The t-table (for the t-distribution) is different from the z-table (for the z-distribution). Make sure you understand the values in the first and last rows. Finding probabilities for various t-distributions, using the t-table, is a valuable statistics skill. The evidence in the trial is your data and the statistics that go along with it. All hypothesis tests ultimately use a p-value to weigh the strength of the evidence (what the data are telling you about the population). The p-value is a number between 0 and 1 and is interpreted in the following way: A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis. If the scatterplot doesn’t show that there’s at least somewhat of a linear relationship, the correlation doesn’t mean much. Why measure the amount of linear relationship if there isn’t much of one? You know that the average length is 7.5 inches, the sample standard deviation is 2.3 inches, and the sample size is 10. This means