Lecture 5 - Biostatistics Part 1-2

Question 1

What are the Measures of Central Tendency?

Answer 1

Mean - the “average” – sum of the set divided by the number in the set

Median – the middle point (arrange the data smallest to largest, then find the middle point)

Mode – the score that occurs most frequently in a set of data
—-May have two most common values = “bimodal distribution”

Question 2

the “average” – sum of the set divided by the number in the set

Answer 2

Mean -

Question 3

– the middle point (arrange the data smallest to largest, then find the middle point)

Answer 3

Median

Question 4

– the score that occurs most frequently in a set of data

Answer 4

Mode

—-May have two most common values = “bimodal distribution”

Question 5

Mode

—-May have two most common values =

Answer 5

“bimodal distribution”

Question 6

• The point/score at which 50% of scores fall below it and 50% fall above it

Answer 6

Median

Question 7

This is the most general and least precise measure of central tendency

When two values occur the same number of times – Bimodal distribution

Answer 7

Mode - most frequently occurring value

Question 8

look at mean median mode images on slide 10

Answer 8

!

Question 9

Standard deviation

Answer 9

a measure of variation of scores about the mean

Question 10

Variance compared to…

Answer 10

standard deviation

Question 11

quantifies the amount of variability, or spread, around the mean of the measurements.

To calculate: take each difference from the mean, square it, and then average the result

Answer 11

Variance (σ2 )

Question 12

To calculate the variance:

Answer 12

take each difference from the mean, square it, and then average the result

Question 13

: a measure of variation of scores about the mean

Answer 13

Standard deviation (σ)

Question 14

To calculate the standard deviation:

Answer 14

take the √ of the variance
(the “average distance” to the mean)

In practice, the standard deviation is used more frequently than the variance.

Primarily because the standard deviation has the same units as the measurements of the mean.

Question 15

When comparing two groups, the group with the larger standard deviation exhibits a greater amount of _____ while the groups with smaller deviation has less _______.

Answer 15

variability (heterogeneous)

variability (homogeneous)

Question 16

Empirical rule for data (68-95-99) - only applies to a set of data having a distribution that is approximately bell-shaped:

Answer 16

Approximately 68% of all scores fall with 1 standard deviation of the mean

Approximately 95% of all scores fall with 2 standard deviations of the mean

Approximately 99.7% of all scores fall with 3 standard deviations of the mean

Question 17

Scatterplots:

A useful summary of a set of ________-

Answer 17

bivariate data (two continuous variables)

Question 18

Scatterplots:

Gives a good visual picture of the relationship between the two variables, and aids the interpretation of the _____

Answer 18

correlation coefficient or regression model.

Question 19

the statistic that summarizes the relationship between the variable on the x axis and the variable on the y axis

Answer 19

correlation coefficient

Question 20

Perfect Positive correlation

Answer 20

X increases and Y increases at the same rate

Question 21

Perfect Negative correlation

Answer 21

X increases and Y decreases yet at the same rate

Question 22

X increases and Y increases =

Answer 22

positive correlation

Question 23

X increases and Y decreases =

Answer 23

negative correlation

Question 24

0 value for correlation coefficient means there is

Answer 24

no correlation

Question 25

Represented by “r ” (rho) The absolute value of the coefficient (its size, not its sign) tells you how strong the relationship is between the variables.

Answer 25

Correlation Coefficient

Question 26

Tells us how strongly two variables are related

Answer 26

Correlation Coefficient

Question 27

Correlation Coefficient “r” can not be > 1 or < -1 Closer to -1 or +1: ? Closer to 0 : ?

Answer 27

Closer to -1 or +1: the stronger the relationship Closer to 0 : the weaker the relationship

Question 28

The most common measure of association. Results can misleading if the relationship is non-linear.

Answer 28

Pearson Correlation

Question 29

______ correlation is very sensitive to outlying values.

Answer 29

Pearson’s

Question 30

______ non-parametric version of Pearson’s correlation. The calculation is based on the ranks of the data points of the x and y values.

Answer 30

Spearman Correlation:

Question 31

The statement that establishes a relationship between variables being assessed Example: In a clinical trial the hypothesis states the new drug is better the placebo

Answer 31

Alternative hypothesis (Ha or H1)

Question 32

The statement of no difference or no relationship between the variables Example: In a clinical drug trial the null hypothesis states that the new drug is no better than placebo

Answer 32

Null hypothesis (Ho)

Question 33

AKA the “research hypothesis”

Answer 33

Alternative hypothesis

Question 34

Hypothesis stating the expected relationship between independent and dependent variables.

Answer 34

Alternative hypothesis

Question 35

If there IS a statistically significant difference, then the researchers “ACCEPT” the alternative hypothesis and “REJECT” the null hypothesis.

Answer 35

Alternative hypothesis

Question 36

If there IS a statistically significant difference, then the researchers must “REJECT” the Null hypothesis

Answer 36

Null hypothesis

Question 37

If there IS NOT a statically significant difference, then the researchers must “RETAIN” or “FAIL to REJECT” the Null hypothesis.

Answer 37

Null hypothesis

Question 38

Two kinds of errors can be made when we conduct a test of hypothesis.

Answer 38

This first is called a Type I error; also known as a rejection error or an α error. The second kind of error that can be made during a hypothesis test is a Type II error, also known as an acceptance error or an β error.

Question 39

A _____ error is made if we reject the null hypothesis when null hypothesis is true.

Answer 39

type I

Question 40

The probability of make a type I error is determined by the ______ of the test.

Answer 40

significance level

Question 41

The second kind of error that can be made during a hypothesis test is a Type II error, also known as an _____ error or an _____ error.

Answer 41

acceptance error or β error

Question 42

A Type 2 error is made if we....

Answer 42

...fail to reject null hypothesis.

Question 43

The probability of committing a type II error is represented by...

Answer 43

the Greek letter β.

Question 44

The probability of finding an effect The probability of correctly rejecting the null hypothesis The probability of seeing a true effect if one exists Designers of studies typically aim for a power of 80% or 0.8 Implies there is an 80% chance of getting it right Generally speaking: More people = more power

Answer 44

Statistical power

Question 45

The probability of correctly rejecting the null hypothesis

Answer 45

Statistical power

Question 46

The probability of seeing a true effect if one exists

Answer 46

Statistical power

Question 47

Designers of studies typically aim for a power of 80% or 0.8 Implies there is an 80% chance of getting it right

Answer 47

Statistical power

Question 48

______ calculates the number of participants a study must have to draw accurate conclusions Takes into consideration: estimated effect size, sample means, etc.

Answer 48

power analysis

Question 49

what does a power analysis take into consideration?

Answer 49

Takes into consideration: estimated effect size, sample means, etc.

Question 50

is the probability of avoiding a type II error.

Answer 50

Power

Question 51

Power may also be thought of as the likelihood that a particular study will detect a _____________ given that one exists.

Answer 51

deviation from the null hypothesis

Question 52

If the β is the probability of making a type II error, 1- β is called the....

Answer 52

power of the test of hypothesis.

Question 53

1- β is called....

Answer 53

the power of the test of hypothesis.

Question 54

Statistical significance and p-value How do we determine if the study result happened by chance alone? What determines statistical “significance”?

Answer 54

Significance The probability of rejecting a true H0 α = .05 usually set, acceptable error -----Chance that 5 times out of 100 the H0 would be falsely rejected

Question 55

Statistical significance and p-value

Answer 55

Probability level The likelihood that the difference observed between two interventions could have arisen by chance Accepted value is 5% risk (p = .05) Means there is a 5% chance that the results happened by chance Allows us to reject or accept the null hypothesis

Question 56

Statistical significance and p-value p is... α is the acceptable error, usually = .05 p ≤ α _____ the H0 (null hypothesis) the results... p > α _____ the H0 (null hypothesis) the results....

Answer 56

the chance of random error α is the acceptable error, usually = .05 p ≤ α reject the H0 (null hypothesis) the results are statistically significant p > α fail reject the H0 (null hypothesis) the results not statistically significant

Question 57

Less than 5% chance the effect happened by chance. “There is less than a 5% chance that the null hypothesis is falsely rejected” Often reported as “significant at the 0.05 level.”

Answer 57

A statistically significant p = or < .05

Question 58

If the number of subjects is small, p value tells us that the effect was either large or consistent (or both) If the number of subjects is large, the effect size may not be that large

Answer 58

A highly significant p < .001

Question 59

If the number of subjects is small, there might not have been enough subjects to find a difference that truly does exist If the number of subjects is large, we can be confident that either there is no difference between treatments, or the treatment effect is not consistent

Answer 59

An insignificant p > .05

Question 60

Statistical significance and p-value Depends on several factors... As all of these factors increase, the likelihood of finding statistical significance increases

Answer 60

How large the effect was How consistent the effect was How many patients were studied ---As all of these factors increase, the likelihood of finding statistical significance increases

Question 61

What's the difference between…. | P value of .051 and .049

Answer 61

Look at the slides if you don't know for sure.... slide 28 in particular