One-Sample
t-Test /
- Tests if the mean of single variable differs from a specified constant
- “Does the average calorie intake of the males in this class significantly differ from the 1200 necessary for growth?"
Two-Sample
t-Test
(Independent) /
- Compares means for two groups
- “Do this year AP Bio Student scores differ from last yearAP Bio student scores?
Matched Paired t-Test /
- Compares the means of two variables for a single group (e.g., before & after treatment)
- “Doeslung capacity improve after an exercise program?
Chi Square (Goodness of Fit) /
- For estimating how closely an observed distribution matches an expected distribution
- You flip a coin 100 times, do you get 45 heads and 55 tails. Is this significantly different than what we would expect (50/50)?
Chi Square
(Independence)
(Pearson) / To examine whether two variables are independent or not. (It cannot tell greater or less only if they are independent or not.) / 2 Categorical / 1 Categorical (counts)
One-way ANOVA / To test the equality of two or more means at one time.
- *note, if means are found to be unequal another test should be run to determine which means are significantly different. These tests are post-hoc analysis such as Tukey HSD, LSD, & Bonferroni
Two-way ANOVA / Examines the influence of two categorical IVs at the same time. / 2 Categorical / 1 Quantitative (means)
T-Values:
The value of t is the result of putting the sample data through the formula for the t-test. The t-value is related to the size of the difference between the means of the two samples you are comparing. The larger t is, the larger the difference. The t-value is not the most useful result to report, which is why we also report p-values.
P-Values:
A p-value answers this question: If my null hypothesis were true, what is the probability of getting a t-value at least as big as mine?. Obviously, the lower this value is, the less likely it is that you would find a difference like yours by chance.
The p-value helps you decide whether or not your data supports the null hypothesis. You make this decision by deciding how low your p-value should be before you will reject the null hypothesis. This cut-off point is called the significance level and is usually set at 0.05 or 0.01.
Sometimes you will see the p value reported as an exact figure, for example, p=0.023. In other places, you will see a less than sign (<), for example, p<0.05. This is because computer programs can calculate the exact value of p, whereas looking up p-values in tables (which is covered at level two of this topic) only allows you to say that the p-value is below one of a few set values. Either method is acceptable, but we will use the less than sign because we use tables at level two. Note also, that software will sometimes report very low p-values, 0.00001, for example, or even p=0. Never report that p=0, this is a side effect of the limited accuracy of some software. If p is less than 0.001, then report p<0.001 rather than the exact p value.
Sample Size:
The more data you have, the smaller your sampling error is likely to be. The degrees of freedom value takes this into account when calculating the p-value.