Understanding Statistical Significance and Hypothesis Testing

Study Notes

Significance is defined as the quality of being statistically significant, denoted by alpha (α) or a symbol, referring to the degree of significance in which we accept or reject the null hypothesis.
In public health research, alpha (α) is usually 0.01 or 1%, in social science, alpha (α) is usually 0.05 or 5%, and in other studies, it is 0.10 or 10%.
This implies that there is a 1%, 5%, or 10% probability of rejecting a true null hypothesis, written as α = 0.01, α = 0.05, or α = 0.10.
The alternative hypothesis is denoted by a symbol, "≠" (not equal), and when the alternative hypothesis is not in class, the symbol is "≠" (not equal).
If the alternative hypothesis is not in class, the alpha level will be divided by 2, so the alpha level for 0.01 divided by 2 is 0.005, for 0.05 divided by 2 is 0.025, and for 0.10 divided by 2 is 0.05.
In a two-tailed test, the alternative hypothesis is two-sided, denoted by "≠" (not equal), and the test is used to determine if the sample mean is significantly different from the population mean.
In a one-tailed test, the alternative hypothesis is one-sided, denoted by "<" (less than) or ">" (greater than), and the test is used to determine if the sample mean is significantly less than or greater than the population mean.
The level of significance is also the probability of making the wrong decision when the null hypothesis is true.
The rejection region is the area under the normal curve where the null hypothesis is rejected.
A confidence interval is a range of values within which the true population parameter is likely to lie.
A 90% confidence interval means that there is a 10% probability of rejecting a true null hypothesis.
A 93% confidence interval means that there is a 7% probability of rejecting a true null hypothesis.
The alpha level for a 93% confidence interval is 0.07.
A one-tailed test is used when the alternative hypothesis is one-sided, and a two-tailed test is used when the alternative hypothesis is two-sided.
The null hypothesis is a statement of no difference or no effect, while the alternative hypothesis is a statement of difference or effect.
The test statistic is used to determine whether to reject or fail to reject the null hypothesis.
The p-value is the probability of obtaining a result as extreme or more extreme than the one observed, given that the null hypothesis is true.
If the p-value is less than the alpha level, the null hypothesis is rejected; otherwise, it is failed to reject.