W4 Standard Error, Confidence interval, Hypothesis & Significant values

Question 1

What does Standard Deviation (SD) provide an indication on?

Answer 1

SD = It provides an indication of how well the mean represents the sample data.

Question 2

What does Standard Error (SE) provide an indication of?

How do you calculate SE of mean?

Answer 2

SE = It provides an indication of how well the sample represents the population
- Divide the SD by the square root of the sample size

Question 3

Why do we use samples?

Answer 3

• because we can’t measure the whole population

Question 4

What do confidence intervals do?

Answer 4

• It’s a way of seeing how well the mean represents the true population mean
• This is another way to see how well the sample represents the population
• It is an estimated range of values which are 95% likely to include the REAL population mean
• Gives you a lower boundary & upper boundary

Question 5

How to calculate a confidence interval:

Answer 5

Lower boundary of 95% CI = X - (1.96 x SE)
Upper boundary of 95% CI = X + (1.96 x SE)
X = mean of the sample

Question 6

What is a hypothesis?

Answer 6

• An estimation or proposed explanation of a theory made on limited evidence.

Question 7

What is correlation (r)?

Answer 7

• Tells us the strength & direction of a relationship/association

Question 8

What is regression?

Answer 8

• Allows one variable to predict the other variable

Question 9

How would you test to see if two means are different?

Answer 9

• Use a independent T-test
  Or
• Paired/dependent T-test

Question 10

What T-test would you use if the means were from two separate groups were different?

Answer 10

• The independent T-test

Question 11

What T-test would you use if the two means are from one group of people but at two different times (E.g. before & after)?

Answer 11

• Paired/dependent T-test

Question 12

What’s a Null Hypothesis?

Answer 12

• States there will be no relationship between the variables or states there will be no difference between the means

Question 13

What’s an Alternative Hypothesis?

Answer 13

• This states that there will be a relationship between the variables or states there will be a difference between the means

Question 14

What are the 6 steps to hypothesis testing?

Answer 14

1. Null Hypothesis
2. Alternative Hypothesis
   - Directional
   - Non-directional
3. Select a level of significance (alpha level)
4. Collect & summarise data
5. Run statistical test
6. Interpret significance of results (p-value)

Question 15

What is the Alpha level (a)?

Answer 15

• Typically set at 5% [a = 0.05]
• This is an error rate associated with incorrectly rejecting the Null hypothesis.
  This means when the Null hypothesis is in reality true we will still (incorrectly) reject the Null hypothesis 5% of the time.

Question 16

What is type 1 error?

Answer 16

• You conclude there is a difference when in reality there isn’t (sampling error unrepresentative samples)

Question 17

What is type 2 error?

Answer 17

• You conclude there is no difference when in fact there is (sample size too small)

Question 18

What is the probability value (p-value or Sig)?

Answer 18

• The p-value provides a measurement of the strength of the evidence against the Null hypothesis

Question 19

If you have a small (p<0.05) probability value (p-value or Sig) does that mean the observed difference was more likely due to chance or not?

Answer 19

• The smaller the probability value (p-value or Sig) the more likely the observed difference was not because of chance.
• Smaller p-value = not chance

Question 20

Examples of Significance testing:
- Once the analysis returns with a p<0.03 we … the Null hypothesis and interpret the difference as … yet, there is still a … percent chance (p<0.03) that the results were due to chance (due to sampling variation).
Fill in the blanks.

Answer 20

• …we reject the Null hypothesis…
• …interpret the difference as ‘real’ (significant)…
• …yet, there is still a 3 percent chance (p<0.03) that the results were due to chance…

Question 21

• What can you assume if you have these p-values?
  1. p<0.10 to p<1
  2. p = 0.05 to 0.10
  3. p<0.05
  4. p<0.01
  5. p<0.001

Answer 21

1. You can assume the Null hypothesis is correct as there’s no evidence against it (no relationship or no difference between means)
2. There is weak evidence against the Null hypothesis but not enough to reject it.
   (3, 4 & 5 is what you want!!)
3. Moderate evidence against the Null hypothesis and in favour of alternative hypothesis
4. Strong evidence against the Null hypothesis and in favour of alternative
5. Very strong evidence against the Null hypothesis and in favour of alternative