Introduction and Basics- Lecture 1

Question 1

3 main roles in statistics

Answer 1

1. Designing experiments
2. Analysing data
3. Drawing conclusions (understanding results)

Question 2

Definitions:
1. Data
2. Statistics
3. Population
4. Sample

Answer 2

1. consists of information that comes from observations, measurements, responses
2. science of collecting, anlaysising and organising data. Involves interpretation
3. collection of all outcomes, responses, measurements that are of interest
4. subset of a population

Question 3

Descriptive statistics

Answer 3

Involves organisation, summarization and display of data: e.g words, graphs, captions, numbers

Question 3

Inferential statistics

Answer 3

Using a sample to interpret the results and draw conclusions about population

Question 4

Design of a statistical study

Answer 4

1. Identify variable of interest and population of the study
2. Detailed plan to collect data- ensure sample is representative of population if using a sample
3. Collect data
4. Describe data
5. Interpret data and make decisions about population using inferential statistics- drawing conclusions
6. Identify possible errors

Question 5

Methods of data collection - Observational study?

Answer 5

Researcher observes and measures characteristics of interest of part of population

Question 6

Methods of data collection - experiment?

Answer 6

Treatment is applied to part of a population, and responses are observed

Question 7

Methods of data collection - simulation?

Answer 7

use of a mathematical or physical model to reproduce the conditions of a situation or process

Question 8

Methods of data collection - survey

Answer 8

investigation of one or more characteristics of a population
1. census = measurement of an entire population
2. sampling = measurement of part of population

Question 9

Defintion - stratified sample?

Answer 9

members from each segment of a population, to ensure each segment is represented

Question 10

Defintion - cluster samples?

Answer 10

all members from randomly selected segments of a population

Question 11

Defintion - systematic samples

Answer 11

each member of the population is assigned a number. Starting number is randomly selected and sample members are selected at regular intervals

Question 12

Defintion - convenience samples?

Answer 12

only of availbale members of the population (can be used as a pilot study but it is not representative of the whole population, will be biased)

Question 13

Discrete variable

Answer 13

indivisible categories e.g class size, number of children in a family

Question 14

Continuous variable

Answer 14

infinitely divisible into whatever units e.g time, weight. Time can be measured to the nearest minute, second, half - second etc.

Question 15

Measuring variables

Answer 15

Requires a set of categories = scale of measurement and a process that classifies each individual into one cateogry

Question 16

4 Types of Measurement scales
1. Nominal scale
2. Ordinal scale
3 Inverval scale
4. Ratio scale

Answer 16

1. unordered set of categories indentified only by name
2. ordered set of categories
3. ordered series of equal-sized categories
4. interval scale where a value of zero indicates none of the variables

Question 17

correlational study

Answer 17

determine whether theres a relationship between 2 variables, describe relationship and observe 2 variables as they exist naturally

Question 18

manipulated variable

Answer 18

independent variable

Question 19

observed variable

Answer 19

dependent variable

Question 20

central value characterisation of whole set of data

Answer 20

measures of central value e.g mean or media must be coupled with measures of data dispersion (average distance from the mean) to indicate how well the central value characterises data as a whole. The smaller the narrow window data, the better the representation of data.

Question 21

center measurement defintion

Answer 21

summary measure of overall level of dataset e.g mode, mean, median

Question 22

median sensitivity?

Answer 22

median is less sensitive to outliers (extreme scores) than the mean, thus better measure than the mean for highly skewed distributions

Question 23

variability (dispersion) measures what?

Answer 23

amount of scatter in a dataset with methods used to represent this: range, variance, IQR, coefficient of variation. Most common is standard deviation

Question 24

what is variance?

Answer 24

variance of set of observations is the average of the squares of the deviations of the observations from their mean

Question 25

standard deviation

Answer 25

square root of the variance and variance showing how the data varies across collection of sample set. Large standard deviation indicates data points are far from the mean

Question 26

data collection and selection of sample sizes makes difference why?

Answer 26

if there are 9 samples, can be assumed as 1 dataset with N=9 BUT can also be assumed as 3 datasets from 3 independent studies, N=3 mean remains the same but changes standard deviation

Question 27

standard error

Answer 27

standard deviation of sample means and a measure of how representative a sample is likely to be of the population

Question 28

large standard error?

Answer 28

a lot of variability between the means of different samples, thus sample might not be representative of population

Question 29

small standard error?

Answer 29

most sample means are similar to the population mean, thus sample is accurate reflection of population

Question 30

frequency distribution- best visualisation of data?

Answer 30

Histogram, but number of bins are important. Histograms not good when you dont have enough data. (too many bins = noisy, too few bins can mask out important features)

Question 31

1.normal distribution, 2.skewed distribution, 3.modality distribution

Answer 31

1. central bellcurve shape uniform 2. shifted to left (positive) or right (negative) 3. 2 efective central values and 2 populations of responses

Question 32

z scores?

Answer 32

used to convert any normal distribution such that: - mean = 0 - standard deviation - 1 important z score: +- 1.96 (removes outlying data- 2.5%)

Question 33

z score calculation?

Answer 33

𝑧=(𝑋−𝑋 ̅)/𝑠

Question 34

null hypothesis?

Answer 34

nothing is happening

Question 35

alternate hypothesis?

Answer 35

what you're expecting to happen is happening, trying to disprove null hypothesis

Question 36

p- value?

Answer 36

Probability that the observed statistic is equal to or more extreme, than observed result then Ho is true. trying to find at which point you have enough evidence against null hypothesis to support actual alternate hypothesis.

Question 37

smaller p value?

Answer 37

swinging against null hypothesis, further towards end of bell curve, stronger evidence against null hypothesis

Question 38

one sided test

Answer 38

in particular condition experiment is set up with, only going one way

Question 39

two sided test

Answer 39

not null hypothesis, can go up or down

Question 40

for one sided test, critical value that represents z score, p value?

Answer 40

either + or - but not both (p<0.5) if z>- 1,645)

Question 41

for two sided test, critical value?

Answer 41

number that separates blue zone (ends of bell curve) from the middle. To be statistically significant, z score needs to be in the blue curve

Question 42

p value larger than 0.05?

Answer 42

large p value, not disproving null hypothesis. Not good indication is that is it 2 significant means.

Question 43

for 2 sided test, where p value is P= 0.037, what do you do and is there is strong evidence for or against null hypothesis, Ho?

Answer 43

If 2 sided, P= 0.037 x 2 = 0.07 Does not swing either way, thus not surveying enough people or greater number of population. With this p-value, cannot say we have enough evidence against null hypothesis. Right on borderline and no strong evidence in either direction

Question 44

difference between p - value and a (alpha)-level?

Answer 44

a- level = indication error and is set before collection of data, to help set up experiment. defines error we are willing to make to say we made a difference. If we're wrong, its an alpha error p- value = calculated after we gather data Calculated probability of a mistake by saying it works e.g level of significance. Descrives percent of population/ area under the curve in the tail that is beyond our statistic

Question 45

a- level is 0.5. Reject Ho when?

Answer 45

P ≤ a so p is smaller than alpha

Question 46

a- level is 0.5. Retain Ho when?

Answer 46

P>a if a -level is small and tight data set, harder to reject null hypothesis

Question 47

B (beta level)?

Answer 47

probability of erroneously retaining Ho

Question 48

Type I error?

Answer 48

erroneous rejection of true Ho

Question 49

Type II error?

Answer 49

erroneous retention of false Ho

Question 50

Power?

Answer 50

1- B (beta) probability of avoiding a type II error (retaining a false null hypothesis 1- B = Pr (reject Ho i I Hfalse)

Question 51

True or False- all variables can be classified as quanititative or categorical value?

Answer 51

True

Question 52

True or False- Categorical values can be continuous variables?

Answer 52

False

Question 53

True or False- quantitative variables can be discrete variables

Answer 53

True

Question 54

inferential statistics

Answer 54

used to make a conclusion about a population based on a sample dataset

Question 55

descriptive statistics

Answer 55

involves the organisation, summarization, and display of data

Question 56

center measurement

Answer 56

summary measure of the overall level of a dataset (mean, median, mode, geometric mean)

Question 57

what is the better measure, mean or median

Answer 57

the median is less sensitive to outliers (extreme scores) than the mean and thus a better measure than the mean for highly skewed distributions

Question 58

variability

Answer 58

measures the amount of scatter in a dataset

Question 59

range

Answer 59

crude measure of variability

Question 59

what does a large standard deviation signify?

Answer 59

the data points are far from the mean

Question 60

p-value in context of null hypothesis

Answer 60

used to quanitfy the idea of statistical significance of evidence

Question 61

why particular p-value

Answer 61

probability that results gained by chance and chance is the only factor

Question 62

single sample

Answer 62

one group; no concurrent control group

Question 63

paired sample

Answer 63

two samples; data points uniquely matched

Question 64

two independent variables

Answer 64

two samples, separate (unrelated) groups

Question 65

Measure vitamin content in loaves of bread and see if the average meets national standards

Answer 65

single sample as just one experiment done and one population

Question 66

Compare vitamin content of loaves immediately after baking versus content in same loaves 3 days later

Answer 66

paired sample as comparison and 2 pairs

Question 67

Compare vitamin content of bread immediately after baking versus loaves that have been on shelf for 3 days

Answer 67

independent as same thing not measured twice. Two groups with different reatments

Question 68

degrees of freedom

Answer 68

number of observations in the data that are free to vary when estimating statistical parameters

Question 69

df conservative

Answer 69

the smaller of (n1 – 1) or (n2 – 1)

Question 70

comparison of means using t statistic

Answer 70

(𝑥 ̄_1−𝑥 ̄_2)±(𝑡_(𝑑𝑓,1−𝛼/2))(𝑆𝐸_(𝑥 ̄_1−𝑥 ̄_2 ))

Question 71

difference between µ and X ̅

Answer 71

µ is the population mean and X ̅ is the sample mean

Question 72

α-level represent?

Answer 72

The probability of erroneously rejecting the null hypothesis

Question 73

A P value of 0.025 indicates the null hypothesis has a 5% chance of being true in a two-tailed test, True or False

Answer 73

False

Question 74

11. A statistically significant difference is determined by

Answer 74

The experimental design when defining α A P-value that is equal to or smaller than α A z-score above the critical value (in a one sided test)

Question 75

T-tests enable a comparison of the means for samples which are:

Answer 75

Degrees of freedom and α

Question 76

We cannot compare all three groups in multiple comparisons, as it will lead to...

Answer 76

Family wise error rate

Question 77

At α = 0.05, the P(retain all three Hos)

Answer 77

(1−0.05)3 = 0.857, so P (reject at least one) = 1−0.847 = 0.143 - This is the family-wise error rate.

Question 78

25. We cannot compare all three groups in multiple comparisons, as it will lead to:

Answer 78

family wise error rate

Question 79

what does a significance level do?

Answer 79

The significance level defines the distance the sample mean must be from the null hypothesis to be considered statistically significant.

Question 80

what does the confidence level do?

Answer 80

The confidence level defines the distance for how close the confidence limits are to sample mean.

Question 81

how to know if you are statistically significant?

Answer 81

1.If the P value is less than your significance (alpha) level, the hypothesis test is statistically significant. 2.If the confidence interval does not contain the null hypothesis value, the results are statistically significant. 3.If the P value is less than alpha, the confidence interval will not contain the null hypothesis value.

Question 82

what are confidence intervals used for?

Answer 82

confidence intervals to assess the precision of the sample estimate. For a specific variable, a narrower confidence interval suggests a more precise estimate of the population parameter than a wider confidence interval

Question 83

Solution to multiple comparisons:

Answer 83

Test for overall significance using a technique called “Analysis of Variance” (ANOVA) Do post hoc comparison on individual groups

Question 84

is regression and correlation inferential or descriptive?

Answer 84

descriptive

Question 85

is anova inferential or descriptive

Answer 85

inferential

Question 86

is the applied to means method inferential or descriptive

Answer 86

inferential

Question 87

what descriptive method is the bivariate and multivariate method part of, respectively?

Answer 87

correlation and regression for bivariate multiple regression for multivariate

Question 88

p value?

Answer 88

The probability that the observed test statistic is equal to or more extreme, than the observed result when Ho is true

Question 89

What is the probability of the observed test statistic when Ho is true?

Answer 89

Probability of observed statistic is very low.

Question 90

𝜇_1−𝜇_2 " is the parameter " True or false?

Answer 90

True

Question 91

𝑥 ̄_1−𝑥 ̄_2 " is the point estimator"

Answer 91

True

Question 92

Ha: μ1 – μ2 > 0 is this left or right tailed

Answer 92

right

Question 93

Ha: μ1 – μ2 < 0 is this left or right tailed

Answer 93

left

Question 94

why do we not perform separate t-tests

Answer 94

Null hypothesis has different arrangements. Cannot treat them as independent samples, have to compare 1, 2 and 3,not each thing individually, because end up acrewing random differences.

Question 95

standard error is computed soley from sample attributes: True or False

Answer 95

True