L5 - Descriptive and Inferential Stats

Question 1

List the type of variables and an example of each

Answer 1

1. Nominal/ Categoriacal
   - Race, Gender
2. Ordinal
   - Pain rating
3. Continuous

Question 2

Describe how you would present numerical data for the following variables:

1. Highest Education Qualification
2. Pain Score
3. Mean Plasma Concentration of Ciprofloxacin

Answer 2

1. n (%)
2. n (%), or % or Median (IQR) where appropriate
3. Mean (SD) or Median (IQR)

Question 3

Common graphical displays that describe the data for the different types of variables

Answer 3

1. Nominal/ Categorical: N.A.
2. Ordinal: pie char, bar chart
3. Continuous: Box plot, Histogram

Question 4

Define Inferential statistics. What is its main assumption?

Answer 4

Stats methods to draw conclusions from sample and imake inferences to an entire ppn

Assumption: Sample represents a RANDOM SAMPLE from underlying (unobserved) ppn

Question 5

Describe the two main approaches to inferential stats

Answer 5

1. Param Estimation: estimate ppn params from sample stats (Point estimate and interval estimate)
2. Hyp testing:to validate supposition based on limited evi, inferred using sample from ppn (Null and Alternative Hyp)

Question 6

What is Sampling Distribution of sample means?

Answer 6

Under Param Estimation:

• Repeated random samples taken
• Means computed for each sample
• Then means of all samples used as data to get point estimate and CI

Question 7

Describe the properties of sampling distribution of the means

Answer 7

1. Mean ≈ ppn mean
2. SD of sample means ≈ Population SD/rt(n), is also SEM (Std error of mean), which is used to get CI

(note: SD only look at one sample, while SEM look at SD of all the samples of the mean)

Question 8

What is SEM?

Answer 8

Estimate precision/reliability of sample as it relates to ppn from which sample was drawn.

i.e. Tells as where TRUE ppn mean may lie, via the CI

Question 9

What is Central Limit Theorem?

Answer 9

Large sample sizes: Mean approx normally distributed, even if each sample amy not be noramlly distributed

Question 10

Describe point estimate and interval estimate (CI)

Answer 10

• Point estimate: single number to estimate param of interest
• CI: Range of reasonable values intended to contain param of interest. Usually 95% confidence

Question 11

What is the width of CI influenced by?

Answer 11

1. Confidence Level (Higher = increased width)
2. Increased n = Decreased width
3. Increased SD = Increased Width

Question 12

Describe the Null and Alternative Hyp

Answer 12

H0: No difference/ relationship/ effect
H1: opposite of H0

Question 13

Define p-value

Answer 13

Probability that observed result occur by chance, assuming H0 true

Question 14

Define the following:

1. a (alpha)
2. B (beta)
3. Type I error
4. Type II error
5. Stats Power

Answer 14

1. a: Significance level of stats test, or chance to commit type I error
2. B: Probability of failing to reject when there is a difference
3. Type I error = a
4. Type II error = B
5. Stats power: Probability of correctly rejecting false H0 when there is effect = 1-B

Question 15

Does statsig = clisig?

Answer 15

NO

Question 16

Considerations for deciding on appropriate stats test when comparing data between / among groups

Answer 16

1. Number of groups being compared
2. Whether groups are independent or pairedrelated
3. Type of variable the data is
   - For continuous: Whether data is normally distributed
4. Whether assumptions for specific stats test are met

Question 17

Describe the two statistical tests for normality and state when to use each of them.

State their Hypotheses as well

Answer 17

1. Shapiro-Wilk test for n<50
2. Kolmogorov-Smirnov test for n≥50

H0: Distribution is normal
H1: Distribution NOT normal

p < 0.05: Sample data is NOT normal

Question 18

Considerations for deciding on appropriate stats test when examining and quantifying degree of LINEAR relationship between two NUMERICAL variables

Answer 18

1. Whether one or both are continuous or ordinal
   - For continuous: check for normality
2. Whether assumptions are met

Question 19

Considerations for deciding on appropriate stats test when ESTIMATING effect of an INDEPENDENT VARIABLE (i.e. predictor variable) (x) on DEPENDENT VARIABLE (i.e. Outcome variable) (y)

Answer 19

1. Whether DEPENDENT variable is continuous or ordinal or nominal
2. Whether assumptions are met