Hypothesis: The hypothesis is a tentative explanation based on observations you have made. Your observations may have been followed up with a search of the literature for more information before you develop your hypothesis.
Example: Men’s hands are larger than women’s hands OR adding fertilizer to a plant makes it grow better.
Null hypothesis: The actual null hypothesis is a more formal statement of your original hypothesis. The null hypothesis is usually written in the following form: There is no significant difference between population A and population B.
Example: There is no significant difference in hand size between males and females. OR There is no significant difference in the growth of fertilized plants vs. unfertilized plants.
The reason we write it in this form is that scientists are basically skeptics and their goal is to prove a hypothesis false. In fact, you can never really prove that a hypothesis is true. In addition, the null hypothesis is used because it allows you to relate your calculations of the difference between the sample means to a standard of zero.
The t-Test: We use this statistical test to compare our sample populations and determine if there is a significant difference between their means. The result of the t-test is a ‘t’ value; this value is then used to determine the p-value (see below).
If we cannot use a statistical test (doesn’t have to be a t-test) to determine whether a significant difference exists, then it becomes difficult to convince other scientists that your research is worth anything.
P-value: The p-value is the probability that ‘t’ falls into a certain range. In other words this is the value you use to determine if the difference between the means in your sample populations is significant. For our purposes, a p-value < 0.05 suggests a significant difference between the means of our sample population and we would reject our null hypothesis. A p-value > 0.05 suggests no significant difference between the means of our sample populations and we would not reject our null hypothesis.
Types of t-tests: There are two types of t-tests, the unpaired and paired t-test that we will use in this course.
Unpaired t-test: This type of t-test is used when you have independent samples. In other words your samples are not directly related to one another. Ex.: Index finger length between males and females.
Paired t-test: In this t-test your samples are related. You collected data before and after some manipulation of your subjects. Ex.: Pulse before and after 3 cups of coffee.
Reference
http://www.nku.edu/~intsci/sci110/worksheets/basic_ttest_info.html
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