Week 6: T-Tests to compare means Flashcards
1
Q
Describe T-test (6 points)
A
- Compares the means of each group
- t-test for independent samples
- Determines if the difference between the means is statistically significant
- Ex. Do midfielders have a greater vertical jump than defenders?
- To determine if significant differences exist, you must compare means.
- You cannot do this by simply observing the means, you must statistically analyze the scores.
2
Q
Describe the two types of T-Test (7 points)
A
- INDEPENDENT GROUPS:
- Differences between means for two groups of subjects on the same test.
- I.E. Vertical Jump = test ; Midfielders/Defenders = 2 groups - DEPENDENT GROUPS:
- When a group of subjects is measured on two different occasions.
- Also called t-test for paired, related, or correlated samples.
- I.E. Vertical Jump = Test; Defenders = Group; Before training period and after training period = occasions
3
Q
Describe hypotheses (3 points)
A
- Hypothesis = a prediction about the relationship between two or more variables.
- Null Hypothesis (H0 ): The hypothesis that predicts there will be no difference between the means of the groups.
- Alternate Hypothesis (H1 ): The hypothesis that predicts there will be a difference between the means of the groups.
4
Q
How do you develop a hypothesis? (10 points)
A
- Make an assumption
- You don’t have to be certain that your hypothesis is correct
- Help you focus your investigation
- Written in the form of a concise statement
- Not written in first person
- It can be tested
- Examples:
- H0 : There will be no difference in the vertical jump height between midfielders and defenders
- H1 : There will be a difference in the vertical jump height between forwards and midfielders.
- H1 :Defenders will have a significantly greater vertical jump height than midfielders.
5
Q
Describe the Level of Significance (6 points)
A
- The probability that the difference in the sets of scores is real as opposed to coincidental.
- Two most common levels of significance are .01 and .05
- .05 or lower = 5% chance
- .01 or lower = 1% chance
- Sociological research p = .05
- Medical research p = .01 or .001 or .0001 L
6
Q
Describe 1 and 2 tailed test (3 points)
A
- Logical decision:
- Two-tailed or two sided test: Difference could be in either direction.
- One-tailed or one sided: Difference could only logically go in one direction or really sure of direction of result.
7
Q
Describe significant difference (7 points)
A
- The p-value is a probability, with a value ranging from zero to one.
- It answers the question ““IS THERE A STATISTICALLY SIGNIFICANT DIFFERENCE BETWEEN TWO MEANS?”
- t Stat > t critical value
- p = 0.041
- Reject Ho “No difference between number of shots on target”
- Accept H1 “significant difference between number of shots on target” *
- Disproved Ho → accept H1
8
Q
Describe the process of reporting t-tests (9 points)
A
- Bar chart with error bars to show difference between means
- Refer to figure before it is included
- Title is below the figure
- Must include whether t-test for equal or unequal variance
- The groups considered
- Whether it was significant or not
- Correct statistical values (t, df, p)
- Mean and standard deviation
- All presented in sentence format
9
Q
Describe Type I Error (6 point)
A
- Reject the null hypothesis and find a difference that is not really there due to chance
- May occur due to:
- Measurement error
- Sample not random
- Improper use of one-tailed test
- Too liberal p-value e.g. p=0.10. 90% chance of being correct. 10% chance of being incorrect
10
Q
Describe Type II Error (6 point)
A
- Accept the null hypothesis as you may not find a difference when there really is a difference
- May occur due to:
- Measurement error
- N too small, low df. Therefore high critical value (table) and need high t stat.
- Treatment and/or intervention not properly applied
- Too conservative p-value e.g. p=0.01. 99% chance of being correct. 1% chance of being incorrect