Yes
At the same level of significance and against the same alternative hypothesis, the two tests are equivalent.
There are several types of hypothesis testing, primarily categorized into two main types: parametric and non-parametric tests. Parametric tests, such as t-tests and ANOVA, assume that the data follows a specific distribution (usually normal). Non-parametric tests, like the Mann-Whitney U test or the Kruskal-Wallis test, do not rely on these assumptions and are used when the data doesn't meet the criteria for parametric testing. Additionally, hypothesis tests can be classified as one-tailed or two-tailed, depending on whether the hypothesis specifies a direction of the effect or not.
A null hypothesis states that there is no relationship between two or more variables being studied. The assumption in science is that the null hypothesis is true until sufficient evidence emerges, though statistical testing, to reject the null and support an alternative hypothesis. The exact statistical test depends on the number and type of variables being tested, but all statistical hypothesis tests result in a probability value (p). Generally, the null is rejected when p < .05 representing less than a 5% chance that the relationship between the variables is due to error. This cutoff - called alpha - can be set lower in certain fields or studies, but rarely is set higher.
T
You use a z test when you are testing a hypothesis that is using proportions You use a t test when you are testing a hypothesis that is using means
The t-test is a statistical method used to determine if there is a significant difference between the means of two groups. It is commonly applied in hypothesis testing to compare sample data against a population or between two sample groups. The t-test accounts for variability and sample size, allowing researchers to infer whether observed differences are likely due to chance. There are different types of t-tests, including independent, paired, and one-sample t-tests, each suited for specific study designs.
The critical ratio in statistics is a measure used to determine the significance of a test statistic in hypothesis testing. It is typically calculated as the ratio of the difference between the sample mean and the population mean to the standard error of the sample mean. A high critical ratio indicates that the sample mean is far from the population mean, suggesting that the null hypothesis may be rejected. This concept is commonly applied in contexts such as t-tests and z-tests to assess the likelihood of observing the sample data under the null hypothesis.
A paired samples t-test is an example of parametric (not nonparametric) tests.
When the null hypothesis is true, the expected value for the t statistic is 0. This is because the t statistic is calculated as the difference between the sample mean and the hypothesized population mean, divided by the standard error, and when the null hypothesis is true, these values should be equal, resulting in a t statistic of 0.
A hypothesis is the first step in running a statistical test (t-test, chi-square test, etc.) A NULL HYPOTHESIS is the probability that what you are testing does NOT occur. An ALTERNATIVE HYPOTHESIS is the probability that what you are testing DOES occur.
It doesn"t you fool
Yes. The hypothesis comes first. That determines the nature of the test.