Case 1: If the t-statistic lies on the horizontal axis at the small bar shown in red (around 0.5) in the picture, our nothing is unusual; data are consistent with the null hypothesis. Case 2: If the t-statistic lies on the horizontal axis at the small bar shown in green (around 2.5), then the data would be fairly unusual -- assuming the null hypothesis is true. So a t-statistic of about 2.5 would cast some reasonable doubt on but a t-statistic of about 0.5 would not cast the null hypothesis reasonable doubt on the null hypothesis. A t-statistic even further to the right would cast even more doubt on the null hypothesis. A little algebra will show that if t = is unusually large, then Note: so is , and vice-versa p-Values
Case 1: If the t-statistic lies on the horizontal axis at the small bar shown in red (around 0.5) in the picture, nothing is unusual; our data are consistent with the null hypothesis. Case 2: If the t-statistic lies on the horizontal axis at the small bar shown in green (around 2.5), then the data would be fairly unusual -- assuming the null hypothesis is true. So a t-statistic of about 2.5 would cast some reasonable doubt on the null hypothesis but a t-statistic of about 0.5 would not cast reasonable doubt on the null hypothesis. A t-statistic even further to the right would cast even more doubt on the null hypothesis. Note: A little algebra will show that if t = is unusually large, then so is , and vice-versa p-Values
WorkshopSlidesDayTwo2017-part3.docx