Final (stats)

Question 1

Table

Answer 1

used to present many numerical values

Question 2

Figure

Answer 2

used to show patterns, trends, or relationships

Question 3

Qualities of a good table

Answer 3

Should be understandable on its own
Includes appropriate title in proper location
Logical format
Justified numbers → decimal points line up
Good / consistent spacing
Legend

Question 4

Qualities of a good figure

Answer 4

Understandable on its own
Axes labels (with units)
Appropriate scaling of axis
Symbols
Customized (not the excel default)
No need for box borders around graph
Trendline should be thicker and clear

Question 5

Figure legends (caption)

Answer 5

The key to understanding a figure
A good figure legend includes:
Title
Materials and methods (description of techniques used)
Results (further explanation of the data)
Definitions (of symbols, patterns, lines, abbreviations, etc).

Question 6

Monty Hall Problem

Answer 6

It involves a scenario where you have a 1/3 chance of initially choosing the door with a prize behind it. When the host reveals one of the other doors with no prize, the probabilities shift. By switching doors, you essentially capitalize on the new information and increase your chances of winning to 2/3.

Question 7

Probability

Answer 7

The degree of certainty or chance that something will happen.

Question 8

Statistics

Answer 8

Help us…
Reduce and describe data
Quantify relationships among data
Determine if sets of data are similar / different

Question 9

Goals of a data analysis

Answer 9

Data reduction (and description)
Reduce measures to make more meaningful
Averages, spread, bar chart / plots / histograms (descriptive)
Easier and more meaningful to read than all the individual data.

Question 10

Establish relationships

Answer 10

Descriptive – describe relationship between two observations
Relationship between height and weight
Casual – did something cause the other

Intervention → caused some response

Inference
Infer outcome from sample to population
Is what we see in sample true in population

Question 11

Purpose of sampling

Answer 11

to approximate a larger population on characteristics relevant to the research question.

Question 12

Histograms

Answer 12

Graphical representations
Mainly represent frequency (# of subjects that fall into a range).
Measures of central tendency

Question 13

Mean

Answer 13

average
x̄ = ΣX / N

Question 14

Median

Answer 14

middle of distribution

Question 15

Mode

Answer 15

most frequently occurring value

Question 16

Range

Answer 16

difference between high and low values in a data set

Question 17

Confidence interval

Answer 17

interval estimate of the population mean (using SEM)

Question 18

Standard Error of the Mean (equation)

Answer 18

standard deviation / √sample size

Question 19

Normal distribution

Answer 19

probability that is symmetric about the mean

Question 20

Kurtosis

Answer 20

measure of outliers in a distribution

High kurtosis → heavy tails or outliers (platykurtic
Low kurtosis → light tails or no outliers (leptokurtic)

Question 21

Standard deviation

Answer 21

Measure of data around the mean
Amount by which every value varies from the mean
How tightly values in dataset are bunched around the mean
Variability of individual observations around a single sample mean

Question 22

Central limit theory

Answer 22

when many samples are drawn from a population, the means of these samples tend to be normally distributed.

Question 23

Empirical rule

Answer 23

for a normal distribution, nearly all data fall within three standard distributions of the mean.

Question 24

Standard error of the mean (SEM)

Answer 24

how close sample values are to the average of all data points
also shows how accurately the average reflects the sample data
essentially compares the experimental mean to the true sample mean

SEM will always be lower than SDEV

the larger the sample, the lower the SEM which is good

Question 25

Confidence intervals

Answer 25

give an estimate of how well the sample mean represents the population mean. Range of likely values for population parameter Uses reliability coefficient (s) and SEM

Question 26

Statistical hypothesis testing

Answer 26

Applies the scientific method to data with random fluctuation

Question 27

The null hypothesis (H0)

Answer 27

effect of data does not represent real effect in hypothesis but is merely a result of random fluctuation. Hypothesis that there will be no difference nor relationship between variables.

Question 28

Alternative hypothesis (Ha)

Answer 28

hypothesis formulated based on existing knowledge, theories, or observations. Difference between variables is specified (one group is greater / uses the other)

Question 29

One Tailed vs. Two Tailed Test

Answer 29

One-tailed → clear directional prediction based on prior knowledge Two-tailed → no specific direction expected / both directions equally plausible The decision to use one tailed vs. two tailed test must be made prior to conducting analysis.

Question 30

P-Value

Answer 30

The p-value is the probability of finding your result when the null hypothesis is true. Computed under the assumption the null is supported Region of high probability = high p-value (shaded blue) Region of low probability = low p-value (shaded gray) if the p-value is 0.05 % that tells us that we have a 5% chance of the data supporting the null hypothesis. the confidence level tells us that given this value, we think that there is a 95 % chance that the data will fall into the alternative hypothesis

Question 31

Parameters of likelihood for observations

Answer 31

called alpha levels pre determined (usually 0.05) Alpha value is a probability value The probability threshold decided is low enough for us to decide the null hypothesis is unlikely to be true. If p-value is less than alpha, it is unlikely the null is true.

Question 32

Significant difference

Answer 32

If p-value is low enough, we reject the null hypothesis and conclude a significant difference. (when p is < a → less than a)

Question 33

Parametric tests

Answer 33

Assumes the sample represents the population Follows a normal population distribution (regular bell shape)

Question 34

Non-parametric tests

Answer 34

No assumptions The area of study is better represented by the median (not the normal distribution) Very small sample size Ordinal or ranked data, or outliers cannot be removed.

Question 35

T-test (overview)

Answer 35

compares the means between two groups Based on t distribution T-value measures the size of the difference relative to variation in sample data.

Question 36

Independent (unpaired) t-test

Answer 36

Grouping categories are independent and unrelated Ex. different people, animals, or things where values of one group do not affect the other.

Question 37

Dependent (paired) t-test

Answer 37

Grouping categories are related Ex. the same person at two points in time. If the t test statistic is greater than the critical value, the null can be rejected. A smaller sample means fatter tails (greater likelihood that values will be outliers → bad thing). A larger sample indicates that the value will be closer to the mean.

Question 38

ANOVA

Answer 38

compares the means among three or more groups

Question 39

Degrees of freedom

Answer 39

Is the freedom to vary n (sample) - 1 = degrees of freedom Indicates the number of independent pieces of information

Question 40

Critical value

Answer 40

AKA THE Z-VALUE a specific value or threshold used to determine the acceptance or rejection of a statistical test or hypothesis

Question 41

Types of error

Answer 41

Type I error (false positive) → rejection of a null hypothesis that is actually true in the population (theres a significance when there actually isn't) Type II error (false negative) → failure to reject a null hypothesis that is actually false in the population (theres no significance when there actually is) Type II is especially a risk when doing multiple t-tests instead of doing ANOVA

Question 42

Bonferroni technique

Answer 42

You reduce the chances of incorrectly rejecting the null hypothesis (type I error) in any of the individual tests, but it also increases the possibility of making a Type II error (false negatives), meaning that you might fail to detect a true effect. Looks at the alpha level and divides that by the number of comparisons being made.

Question 43

Downsides of just an ANOVA test

Answer 43

Doesn’t tell us which means are different, it only determines that there is a difference. Hence, we can follow that with a post-hoc test. They help identify where the significant differences lie, providing more specific and detailed information about the relationships between the groups or conditions being compared

Question 44

Correlation

Answer 44

Measures the association of two variables Uses correlation when we want to quantify the strength and direction of a relationship.

Question 45

Depictions of correlations

Answer 45

r < 0.30 → weak to no correlation r = 0.60 → moderate to strong relationship r > 0.70 → substantial to very strong relationship

Question 46

r

Answer 46

correlation coefficient Refers to a measure of the strength and direction of the linear relationship between two variables. It ranges between -1 and 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship. Essentially it tells you strength (magnitude) and direction (positive or negative sign) for the relationship. The Pearson correlation coefficient is the specific calculated value.

Question 47

r^2

Answer 47

coefficient of determination The amount of variance in one variable that is explained or predicted by variance in another variable. It ranges between 0 and 1, where 0 indicates that the independent variables explain none of the variability in the dependent variable, and 1 indicates that the independent variables explain all of the variability.

Question 48

b

Answer 48

slope

Question 49

a

Answer 49

slope

Question 50

Best straight line fit

Answer 50

Minimize the sum of the squared difference between data and curve fit line. y = mx + b

Question 51

Single vs. multiple correlations

Answer 51

Single correlation refers to the relationship between two variables, typically measured using the Pearson correlation coefficient (r-value) Multiple correlation refers to the relationship between a dependent variable and multiple independent variables.

Question 52

Type I Error

Answer 52

The probability of committing a type I (rejected the null but it’s actually true) error is whatever our alpha value is set to. Ex. for an alpha value of 0.05, we have a 5% chance of committing type I error.

Question 53

Type II Error

Answer 53

The probability of committing a type II error (failure to reject the null when it is false) is denoted by beta, which has to do with power (its typical value is 0.8 → 80% chance we are sure we aren't committing a type II error). Beta is the probability that the experiment will yield a not significant result High power = high chance that your experiment will find a statistically significant result when one is present.

Question 54

Power

Answer 54

the probability of rejecting the null hypothesis when it is false (good thing). Is the probability (can’t be negative)... Of making a correct decision That a significance test will pick up an effect that is present Of avoiding a type II error

Question 55

Effect of Power On: - effect size - sample size - sample variance - alpha level

Answer 55

Effect size Large discrimination (shown in bottom right) indicates that we won’t need much power to be sure that the groups are different since they are more spread out and distinct. Hence, more power is needed to detect smaller differences. Sample size Smaller sample sizes require larger amounts of power to detect differences Sample variance Higher variance yields small amounts of power. Alpha value Alpha level is proportional to power lowering the alpha value increases the strictness of the test, making it harder to reject the null hypothesis

Question 56

Diagnostic tests

Answer 56

used to determine the presence or absence of a particular condition in an individual. Validity is evaluated by a test’s ability to assess the presence (sensitivity) or absence (specificity) of a medical condition. Tries to answer a yes or no, often from a non-binary variable. Thus, there must be a cut off point to help create a yes or no answer.

Question 57

True positive

Answer 57

test predicts condition and they have condition

Question 58

False positive

Answer 58

test predicts condition but they do not have condition

Question 59

False negative

Answer 59

test predicts no condition but the have condition

Question 60

True negative

Answer 60

test predicts no condition and they do not have condition

Question 61

Prevalence

Answer 61

portion of population that has a condition (true positive + false negative) / everyone (total population)

Question 62

Sensitivity

Answer 62

proportion of people with conditions that test positive (relative to all individuals with the condition). True positives / total people with condition (TP + FN)

Question 63

Specificity

Answer 63

proportion of people without condition that test negative (relative to all individuals without the condition) True negatives / total people without condition (TN + FP)

Question 64

Positive predictive value

Answer 64

proportion of people with condition that tested positive for the condition (relative to all p tests). True positives / total positives (TP + FP)

Question 65

Negative predictive value

Answer 65

proportion of people without condition who test negative for the condition (relative to all negative tests) True negatives / total negative tests (TN + FN)

Question 66

Accuracy

Answer 66

ability to identify true results (True positives + true negatives) / total number of tests (TP + FP + TN + FN)

Question 67

Prevalence

Answer 67

proportion of the population that has a condition (True positive + false negative) / total population

Question 68

z-value

Answer 68

related to confidence intervals tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean

Question 69

how to calculate confidence interval

Answer 69

CI % = x +/- z*(s/√n) x = sample mean (overall and stays consistent) z = z-value typically taken from a graph. corresponds to the desired confidence interval % s = standard deviation n = sample output is a range

Question 70

z-value at each confidence interval

Answer 70

99% --> 2.576 95% --> 1.96 90% --> 1.645

Question 71

percentage of common association equation

Answer 71

r value * 100

Question 72

how do t-stat and critical value effect the acceptance or rejection of the critical value

Answer 72

t test statistic is greater than the critical value, the null can be rejected.