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.
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2
Q

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

A
  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
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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.
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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.
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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
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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.
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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
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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
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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
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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
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