If the absolute value of your test statistic is greater than the critical value, you can declare statistical significance and reject the null hypothesis. Figure A shows that results of a one-tailed Z-test are significant if the test statistic is equal to or greater than 1.
Figure B shows that results of a two-tailed Z-test are significant if the absolute value of the test statistic is equal to or greater than 1. In hypothesis testing, there are two ways to determine whether there is enough evidence from the sample to reject H 0 or to fail to reject H 0.
However, you can also compare the calculated value of the test statistic with the critical value. The following are examples of how to calculate the critical value for a 1-sample t test and a one-way ANOVA. This gives you an inverse cumulative probability, which equals the critical value, of 1. If the absolute value of the t-statistic is greater than this critical value, then you can reject the null hypothesis, H 0 , at the 0.
Because the P-value approach requires just one computation, most statistical software and calculators use the P-value approach for hypothesis testing. The P-value is the probability of obtaining a test statistic as extreme as the one for the current sample under the assumption that the null hypothesis is true. David Gurney, Created with GeoGebra. Sorry, the GeoGebra Applet could not be started. It is also called the significance level.
The significance level is a threshold we set before collecting data in order to determine whether or not we should reject the null hypothesis. We set this value beforehand to avoid biasing ourselves by viewing our results and then determining what criteria we should use.
There are two criteria we use to assess whether our data meet the thresholds established by our chosen significance level, and they both have to do with our discussions of probability and distributions. Recall that probability refers to the likelihood of an event, given some situation or set of conditions.
In hypothesis testing, that situation is the assumption that the null hypothesis value is the correct value, or that there is no effect.
The value laid out in H0 is our condition under which we interpret our results. To reject this assumption, and thereby reject the null hypothesis, we need results that would be very unlikely if the null was true.
Now recall that values of z which fall in the tails of the standard normal distribution represent unlikely values.
Any result which falls in that region is sufficient evidence to reject the null hypothesis.
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