P value one tailed hypothesis test calculator
We will use the z-statistic because we are assuming we know the standard deviation of the population (5.0 ug/L). Many statisticians consider a p-value less than 0.05 to be statistically significant (and a p-value of 40 ug/Lĥ. The smaller the p-value, the stronger the evidence against the H0 provided by the data. The probability, assuming Ho is true, that the test statistic would take a value as extreme or more extreme than that actually observed is called the p-value of a test. In the words of Moore, McCabe and Craig (2012, p. It is VERY IMPORTANT to know that the p-value is a conditional probability–a probability conditioned on the assumption that the NULL HYPOTHESIS is true.
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For a two-sided test, the two-sided p-value is the probability that the test statistic is greater than OR less than the calculated value. A student t table can be found at this Texas A & M Statistics website.Ī one-sided p-value is the probability that the test statistic is greater than (or less than) the calculated value. With the t-statistic, we assume that we do NOT know the standard deviation of the population (σ) and so we estimate the standard error using the sample standard deviation. With the t-statistic, the standard deviation of the population is estimated with the standard deviation of the sample. With the z-statistic, the standard error equals the standard deviation of the population (σ) divided by the square root of the sample size. In essence, the test statistic calculates how many standard errors the mean of the sample is away from the value that we hypothesize. The standard error is the standard deviation of the sampling distribution of the sample mean. In general terms, a comparison of means test equals: Due to this estimation, we must use the t-distribution which is thicker in the tails to account for estimating the standard error with the sample standard deviation. If the standard deviation is not known, then the standard error must be estimated using the standard deviation of the sample(s). The null and alternative hypotheses should reflect whether or not you are using a one- or two-sided comparison of means test.Ī z-statistic should be calculated when the standard deviation of the population(s) is known. If you want to test whether there is a difference between two means (without any directionality), then you use a two-sided test (and subsequently a tw0-sided p-value (see below). If you want to test whether the mean of population A is greater (or less) than the mean of population B, this is a one-sided test. A one-sided test (leading to a one-sided p-value) examines whether one mean is greater (or less than) the other mean. Two-Sided Comparison of Means Testsįor a comparison of means test, you may use either a one-sided or two-sided test. Example: a comparison of NOx emissions from randomly selected automobiles before and after an additive is added to the fuel. Paired or Repeated measure test: This test compares paired data, such as data collected before and after a treatment. Comparing GRE scores between men and women is an example of a two independent sample test. Two independent sample test:In this test, we collect two independent samples to test whether there is a difference in means between two populations (or if one population mean is greater or less than the other). For example, we might be interest in knowing whether the dissolved oxygen levels in a lake meet a state standard of 5 mg/L. One sample test: We make an inference to a population in comparison to some set value. In each of the tests we make inferences to a population or populations based on one or two samples. It is important to be able to differentiate between these three tests. There are three major types of comparison of means tests: (1) one sample test (2) two independent samples and (3) paired or repeated measures test.
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Interpret the p-value in terms of the hypotheses established prior to the test. Determine p-value from the test statistic using the appropriate z or t distribution.ġ1. Calculate standard deviation of sample IF using a t-test.ġ0. Decide whether a z-statistic or t-statistic is appropriate.ħ. Establish null and alternative hypotheses.ĥ. Examine the appropriateness of a comparison of means test (based on the assumptions)***.Ĥ. Decide whether a one- or two-sided test.ģ.
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(one sample, two sample, paired samples)Ģ. General Steps in Conducting a Comparison of Means Testġ. Understand when to use the Student’s t or the z statistic in a comparison of means test. For an example of the two sample Welch’s test, click here.Ĥ. While you will not be asked to calculate a two independent sample test statistic, you should be able to properly interpret a comparison of means test for two independent samples (understand/interpret hypotheses, test statistic and p-value). Conduct and properly interpret a one sample test.ģ. Understand the conceptual difference among a one sample, two independent sample vs.