WEEK 2: CONFIDENCE INTERVAL, CORRELATION AND REGRESSION

Question 1

What is a point estimator?

Answer 1

It is a single number that estimate plausible value of a population parameter

Question 2

What are characteristics of a good point estimator?

Answer 2

*Unbiased
*Consistent
*Precise ( small standard error)

Question 3

Outline examples of point estimators?
What parameters they measure?

Answer 3

*Sample variance- Population variance
*Sample standard deviation- Population standard deviation
*Sample mean- Population mean
*Sample mode- Population mode

Question 4

What is an interval estimator?

Answer 4

A pair of point estimators between which the population parameter of interest resides in

Question 5

What is a characteristic of a good point interval?

Answer 5

*Short
*Contain population parameter (θ) with high probability

Question 6

What is a significance level of an interval estimator (a) ?

Answer 6

It is a value that is used to determine CI with probability 1-a

Question 7

State the 4 factors that affect the range of Confidence interval range

Answer 7

*Confidence level ( 80,90,95,99 probability)
*Number of samples
*Standard deviation of sample

Question 8

What is the relationship between confidence interval range and width and confidence level?

Answer 8

As the confidence level increase, the confidence interval range and width increase.

Question 9

State the assumptions for the Confidence interval of the mean

Answer 9

• samples were randomly selected
  *The underlying distribution is Gaussian distribution
  *Samples were independently selected from the population

Question 10

What is the formula for calculating CI for 95%?

Answer 10

To calculate 95% confidence interval:

𝜃± 1.96 ∗ (𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟)

Standard error= standard deviation/ square root of the sample size

Question 11

In a random sample of 36 MBBS1 year 1 students, the mean height was 168cm with a standard deviation of 14cm.

Determine a 95% confidence interval for the mean height of all University of Botswana students.

Answer 11

𝜃=168cm, SD=14, sample size (n) =36

95% CI = (168 ±1.96*standard error)

𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟 =14/ square root of 36 = 2.33
∴ 95% 𝐶𝐼 = 168 ± 1.96 ∗ 2.33
∴ 95% 𝐶𝐼 = 168 ± 4.57 𝑜𝑟 [163.43, 172.57]

Question 12

In a random sample of 100 patients at Princess Marina Hospital (PMH), 11% of the patients are allergic to penicillin.

Determine a 95% confidence interval for the proportion of patients at PMH that are allergic to penicillin.

Answer 12

Ƹ=11% or 0.11, sample size (n) =100
95% CI for proportion = (Ƹ ±1.96*standard error for Proportions (SEP))

𝑤ℎ𝑒𝑟𝑒 𝑆𝐸𝑃 =𝑝∗(1−𝑝) 𝑛
=0.11∗ (1−0.11)100
= 0.031289

∴ 95% 𝐶𝐼 = 0.11 ± 1.96 ∗ 0.031289
∴ 95% 𝐶𝐼 = 0.11 ± 0.061 𝑜𝑟 [0.0487, 0.1713]

Question 13

What is standard error?

Answer 13

A value indicating error when a sample mean is used as a point estimator of the population mean

Question 14

State the formula for calculating standard error

Answer 14

𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟 =𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛/ 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒 square root

Question 15

What is association between variables?

Answer 15

The extent to which any two variables are related or correlated.

Question 16

What is Correlation?

Answer 16

Describes the strength of linear association of variables

Question 17

What do the following signs for correlation mean?
+, -, 0

Answer 17

+: perfect positive correlation
-: reverse relationship/ negative association
0: no linear association

Question 18

How to determine whether the correlation is statistically significant if you have r- value without p-value or CI?

Answer 18

Use rule of thumb: the modulus of r must be greater than 2 divided by square root of sample size

r> 2/√sample size OR r<- 2/√ sample size

Question 19

Pearson’s correlation coefficient

Answer 19

Uses linear relationship

Question 20

Spearmen’s correlation coefficient

Answer 20

*Tests monotonic relationship
*Uses non- parametric computation of Pearson’s correlation coefficient that uses ranges to determine the degree of association between variables

Question 21

When to use spearmen’s correlation coefficient?

Answer 21

• If data seems to exhibit non-linear relationship
  *If at least one variable is ordinal
  *If data has outliers

Question 22

How to determine causal relationship between variables?

OR

How would you show that changes in one variable would cause changes in another variable?

Answer 22

Use linear regression

Y=mx+c

Question 23

What is the difference between correlation and regression?

Answer 23

Correlation: describes the strength of linear association between variables
Regression: expresses the relationship between variables in the form of an equation