Week 6: T-Tests to compare means

Question 1

Describe T-test (6 points)

Answer 1

• 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.

Question 2

Describe the two types of T-Test (7 points)

Answer 2

1. INDEPENDENT GROUPS:
   - Differences between means for two groups of subjects on the same test.
   - I.E. Vertical Jump = test ; Midfielders/Defenders = 2 groups
2. 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

Question 3

Describe hypotheses (3 points)

Answer 3

• 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.

Question 4

How do you develop a hypothesis? (10 points)

Answer 4

• 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.

Question 5

Describe the Level of Significance (6 points)

Answer 5

• 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

Question 6

Describe 1 and 2 tailed test (3 points)

Answer 6

• 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.

Question 7

Describe significant difference (7 points)

Answer 7

• 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

Question 8

Describe the process of reporting t-tests (9 points)

Answer 8

• 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

Question 9

Describe Type I Error (6 point)

Answer 9

• 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

Question 10

Describe Type II Error (6 point)

Answer 10

• 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