null hypothesis that p = pi ( Armitage and Berry, 1994 Gardner and Altman, 1989).Ĭonsider using mid-P values and intervals when you have several similar studies to consider within an overall investigation ( Armitage and Berry, 1994 Barnard, 1989). You are also given exact P and exact mid-P hypothesis tests for the proportion in comparison with an expected proportion, i.e. StatsDirect provides an exact confidence interval and an approximate mid-P confidence interval for the single proportion. Some authors refer to this method as a "binomial test". The sign test is basically a single proportion test based on pi = 0.5. The expected proportion (pi) is the probability of success on each trial, for example pi = 0.5 for coming up heads on the toss of a coin. This function compares an observed single binomial proportion with an expected proportion.Įxpected proportion (binomial parameter) = pi If the p-value is “beyond” your alpha level, you would reject the H 0and conclude that there is evidence for a relationship between X and Y.Menu location: Analysis_Proportions_Single. With the p-value we can conclude on the likelihood of getting the slope you get from your sample data due to chance alone. Hypothesis test for the slope in MS Excel can be run through Data > Data Analysis > Regression, where the p-value is given.
Hypothesis test for the slope in MS Excel There definitely seems to be a relationship between X and Y. This extremely low p-value expresses that it would be extremely unlikely to see the increase of our line is due to chance alone. We have very strong evidence that the true slope is not zero and that therefore is a relationship between X and Y. This is an extremely low p-value giving us very high evidence against the H 0 hypothesis and thus against the claim that there is no relationship. We therefore reject the null hypothesis concluding that the provided data indicates that there is a strong relation between X and Y.Īs the table shows the p-value for our data is 1.15 × 10 -7 = 0.000000115. The critical t-value for df = 13 at an alpha level of 0.05 is 2.160 (t-table or statistical software), and our t-statistic = 10.402 which is “far” beyond this critical value. In case, we test for another value, this value is applied instead of the 0.īack to the home-made example where we explore the relationship between persons’ height and their size of gloves:Īs explained in Standard error of the slope and Confidence intervals for the slope, we first calculate the sample standard deviation which then is plugged into the SE formula, and with the SE, we can calculate the t-statistic: As the hypothesized value typically will be 0, we can write as expressed below.
The formula of the t-statistics says: β̂ 1 minus the hypothesized value, divided by the SE. When conducting a hypothesis test for the slope, the null hypothesis claims that there is no linear relationship between X and Y: We recall our estimated regression model: If the slope is 0, it means that our sample statistics indicate no relationship. Therefore, a hypothesis test for the slope (β̂ 1)=0 is the most common, but we can test for any value. We pretend to be as confident as possible about this relationship which is expressed by the slope. The main purpose of regression analysis is to explore the relationship between the explanatory variable (X) and the dependent variable (Y). The purpose of hypothesis testing for the slopeĪ hypothesis test for the slope is based on the fundamentals of hypothesis testing.