STATS Lec 4- P value continued

Question 1

How to find the P-value

Answer 1

• Use statistical tables
  
  • Calculate your test statistics
  • Calculate your degrees of freedom
    
    • number of values in the final calculation of a statistic that are free to vary
    • The number of independent ways by which a dynamic system can move without any constraint imposed on it is called degrees of freedom
  • Compare with the critical value for the statistic in the correct table
  • Gives values for P<0.05, P<0.01 and P<0.001
• Use a computer
  
  • Gives exact P value

Question 2

What test?

Answer 2

• Depends on the design
  
  • Within-subject/repeat measures etc
• Depends on the data type
  
  • Normal, ordinal, bivariate
• We shall discuss those tests based on the normal distribution just now

Question 3

Test: One-tailed, 2 tailed

Answer 3

• Tests based on the normal distribution
  
  • 95% of data within +/- 1.96 S.D of the mean
• 5% chance that a value outside of +/- 1.96 S.D. is from the same population
  
  • So if a value is +/- 1.96 S.D. of the mean, we can REJECT the null hypothesis with 5% chance of being wrong
• A normal distribution is symmetrical about the mean
  
  • TWO tailed: value can be greater or less
  • ONE tailed: Value can be only greater or less

Question 4

Two-tailed hypotheses

Answer 4

• The difference could be in either direction
• Eating sprouts alter your IQ
  
  • Could be higher or lower
• Attending lectures changes your examination mark
• Adding a constituent to broth changes the microbial growth

Question 5

Examples of one-tailed hypotheses

Answer 5

• Chances that girls hair is longer than average
• Eating sprouts increase your IQ
• Missing lectures decreases your examination mark
• Listening to Mozart increases your IQ

Question 6

One-tailed hypothesis

Answer 6

• Data still normally distributed
• 95% of data falls below (or above) a single point- therefore an extra 5% of data that could be part of the population is on one side (above or below dependent on you one-tailed hypothesis)
• 5% may have a value above that by chance
• Any value above the critical value (Z= 1.65) there is a 5% chance that this value is from the population, therefore, there is a 5% chance that if we reject the null hypothesis we will be incorrect (we saying its different not in population)

Question 7

The logic of statistical testing

Answer 7

• We always test the NULL hypothesis and accept or reject the NULL hypothesis
• The NULL hypothesis states that any pattern in the data is no greater than that we might expect by chance (sampling error) alone
• We calculate the probability (p-value) of being wrong if we reject the NULL hypothesis, assuming the NULL is true (type I error)
  
  • A smaller p value= less probability of being wrong
• To lower the possibility of a type I error we can use a more strict probability level e.g. p<0.01- (BUT this increase the probability of a type II error)
• As P value goes down the probability of making a type 2 error goes up (addition rule)