Hypotheses are are the heart of much social research. Here's some useful notes about them.

The power is about 0. Significance Tests for Unknown Mean and Unknown Standard Deviation In most practical research, the standard deviation for the population of interest is not known.

In this case, the standard deviation is replaced by the estimated standard deviation salso known as the standard error. Since the standard error is an estimate for the true value of the standard deviation, the distribution of the sample mean is no longer normal with mean and standard deviation.

Instead, the sample mean follows the t distribution with mean and standard deviation. The t distribution is also described by its degrees of freedom.

For a sample of size Hyphothesis for, the t distribution will have n-1 degrees of freedom. The notation for a t distribution with k degrees of freedom is t k.

As the sample size n increases, the t distribution becomes closer to the normal distribution, since the standard error approaches the true standard deviation for large n. The test statistic follows the t distribution with n-1 degrees of freedom.

The test statistic z is used to compute the P-value for the t distribution, the probability that a value at least as extreme as the test statistic would be observed under the null hypothesis. Example The dataset "Normal Body Temperature, Gender, and Heart Rate" contains observations of body temperature, along with the gender of each individual and his or her heart rate.

The t test statistic is equal to This result is significant at the 0.

Data presented in Mackowiak, P. Matched Pairs In many experiments, one wishes to compare measurements from two populations.

This is common in medical studies involving control groups, for example, as well as in studies requiring before-and-after measurements. Such studies have a matched pairs design, where the difference between the two measurements in each pair is the parameter of interest.

Analysis of data from a matched pairs experiment compares the two measurements by subtracting one from the other and basing test hypotheses upon the differences.

Usually, the null hypothesis H0 assumes that that the mean of these differences is equal to 0, while the alternative hypothesis Ha claims that the mean of the differences is not equal to zero the alternative hypothesis may be one- or two-sided, depending on the experiment. Using the differences between the paired measurements as single observations, the standard t procedures with n-1 degrees of freedom are followed as above.

Example In the "Helium Football" experiment, a punter was given two footballs to kick, one filled with air and the other filled with helium. The punter was unaware of the difference between the balls, and was asked to kick each ball 39 times.â€¢Alternative hypothesis is odds of infection are higher for the group drinking the placebo (juice/placebo.

A P-value (or probability value) is the probability of getting a value of the the sample test statistic that is at least as extreme as the one found from the sample data, assuming that the null hypothesis is true.

Alternative hypothesis definition, (in the statistical testing of a hypothesis) the hypothesis to be accepted if the null hypothesis is rejected.

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Get Started. The documentary hypothesis (DH) is one of four models used to explain the origins and composition of the first five books of the Bible, as well as the most widespread and commonly agreed upon of the various hypotheses.

The first five books of the Bible are Genesis, Exodus, Leviticus, Numbers, and Deuteronomy, called collectively the Torah or Pentateuch. Hypothesis antonyms. Top antonyms for hypothesis (opposite of hypothesis) are proof, reality and truth.

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New Hypothesis Explains Why We Sleep - Scientific American