Statistics Flashcards

Question

Probability

Answer 1

A number between zero and one, inclusive, that gives the likelihood that a specific event will occur

Answer 2

The number of successes divided by the total number in the sample

Answer 3

Data that has an attribute whose value is indicated by a label

Answer 4

Quantitative (an attribute whose value is indicated by a number) data can be separated into two subgroups: discrete and continuous. Data is discrete if it is the result of counting (such as the number of students of a given ethnic group in a class or the number of books on a shelf). Data is continuous if it is the result of measuring (such as distance traveled or weight of luggage).

Answer 5

The act of organizing experimental units into treatment groups using random methods

Answer 6

A method of selecting a sample that gives every member of the population an equal chance of being selected.

Answer 7

The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes to the total number of outcomes

Answer 8

A subset of the population that has the same characteristics as the population

Answer 9

The dependent variable in an experiment; the value that is measured for change at the end of an experiment

Answer 10

A subset of the population studied

Answer 11

The natural variation that results from selecting a sample to represent a larger population; this variation decreases as the sample size increases, so selecting larger samples reduces sampling error.

Answer 12

Once a member of the population is selected for inclusion in a sample, that member is returned to the population for the selection of the next individual.

Answer 13

A member of the population may be chosen for inclusion in a sample only once. If chosen, the member is not returned to the population before the next selection.

Answer 14

A straightforward method for selecting a random sample; give each member of the population a number. Use a random number generator to select a set of labels. These randomly selected labels identify the members of your sample.

Answer 15

A numerical characteristic of the sample; a statistic estimates the corresponding population parameter. sample estimate = parameter + bias + chance error/sampling error

Answer 16

A method for selecting a random sample used to ensure that subgroups of the population are represented adequately; divide the population into groups (strata). Use simple random sampling to identify a proportionate number of individuals from each stratum.

Answer 17

A method for selecting a random sample; list the members of the population. Use simple random sampling to select a starting point in the population. Let k = (number of individuals in the population)/(number of individuals needed in the sample). Choose every kth individual in the list starting with the one that was randomly selected. If necessary, return to the beginning of the population list to complete your sample.

Answer 18

Different values or components of the explanatory variable applied in an experiment

Answer 19

A characteristic of interest for each person or object in a population.

Answer 20

A graph that gives a quick picture of the middle 50% of the data plus the minimum and maximum value.

Answer 21

The value that is the median of the of the lower half of the ordered data set

Answer 22

A graph that shows the frequencies of grouped data. It is a type of frequency diagram that plots the midpoints of the class intervals against the frequencies and then joins up the points with straight lines.

Answer 23

A data representation in which grouped data is displayed along with the corresponding frequencies

Answer 24

A graphical representation in x-y form of the distribution of data in a data set; x represents the data and y represents the frequency, or relative frequency. The graph consists of contiguous rectangles - the area of each representing the percent of the data that block/class represents.

Answer 25

The range of the middle 50 percent of the data values; the IQR is found by subtracting the first quartile from the third quartile.

Answer 26

Also called a class interval; an interval represents a range of data and is used when displaying large data sets

Answer 27

The sum of all values in the population divided by the number of values

Answer 28

A number that separates ordered data into halves; half the values are the same number or smaller than the median and half the values are the same number or larger than the median. The median may or may not be part of the data.

Answer 29

The mean of an interval in a frequency table

Answer 30

The value that appears most frequently in a set of data

Answer 31

An observation that does not fit the rest of the data. Standard test: if data is 2 standard deviations or more

Answer 32

Two data sets that have a one-to-one relationship so that 1) each data set is the same size and 2) each data point in one data set is matched with exactly one data point in the other data set.

Answer 33

A number that divides ordered data into hundredths; percentiles may or may not be part of the data. The median of the data is the second quartile and the 50th percentile. The first and third quartiles are the 25th and the 75th percentiles, respectively. FORMULA 1: Percentile given Percentile Rank of Value P(x) = (n/N)*100, where n = values below x FORMULA 2: Percentile Rank given percentile n = (P*N)/100

Answer 34

The numbers that separate the data into quarters; quartiles may or may not be part of the data. The second quartile is the median of the data.

Answer 35

Used to describe data that is not symmetrical; when the right side of a graph looks “chopped off” compared the left side, we say it is “skewed to the left.” When the left side of the graph looks “chopped off” compared to the right side, we say the data is “skewed to the right.” Alternatively: when the lower values of the data are more spread out, we say the data are skewed to the left. When the greater values are more spread out, the data are skewed to the right. Outliers in the tail pull the mean from the center towards the longer tail.

Answer 36

A number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation. Measures the average deviation of the values from the average SD = the rms size of the deviations from the average Measures how far away values are from the mean on average Deviation = Value - Average SD = sqrt(avg(deviations^2))

Answer 37

Mean of the squared deviations from the mean, or the square of the standard deviation; for a set of data, a deviation can be represented as x – x¯ where x is a value of the data and x¯ is the sample mean. The sample variance is equal to the sum of the squares of the deviations divided by the difference of the sample size and one.

Answer 38

An outcome is in the event A AND B if the outcome is in both A AND B at the same time.

Answer 39

The complement of event A consists of all outcomes that are NOT in A.

Answer 40

The method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; the table provides an easy way to calculate conditional probabilities.

Answer 41

The likelihood that an event will occur given that another event has already occurred

Answer 42

If two events are NOT independent, then we say that they are dependent.

Answer 43

Each outcome of an experiment has the same probability.

Answer 44

A subset of the set of all outcomes of an experiment; the set of all outcomes of an experiment is called a sample space and is usually denoted by S. An event is an arbitrary subset in S. It can contain one outcome, two outcomes, no outcomes (empty subset), the entire sample space, and the like. Standard notations for events are capital letters such as A, B, C, and so on.

Answer 45

A planned activity carried out under controlled conditions

Answer 46

The occurrence of one event has no effect on the probability of the occurrence of another event. Events A and B are independent if one of the following is true: P(A|B) = P(A) P(B|A) = P(B) P(A AND B) = P(A)P(B)

Answer 47

Two events are mutually exclusive if the probability that they both happen at the same time is zero. If events A and B are mutually exclusive, then P(A AND B) = 0.

Answer 48

An outcome is in the event A OR B if the outcome is in A or is in B or is in both A and B.

Answer 49

A particular result of an experiment

Answer 50

The set of all possible outcomes of an experiment

Answer 51

The useful visual representation of a sample space and events in the form of a “tree” with branches marked by possible outcomes together with associated probabilities (frequencies, relative frequencies)

Answer 52

The visual representation of a sample space and events in the form of circles or ovals showing their intersections

Answer 53

an experiment with the following characteristics: 1. There are only two possible outcomes called “success” and “failure” for each trial. 2. The probability p of a success is the same for any trial (so the probability q = 1 − p of a failure is the same for any trial).

Answer 54

A statistical experiment that satisfies the following three conditions: 1. There are a fixed number of trials, n. 2. There are only two possible outcomes, called "success" and, "failure," for each trial. The letter p denotes the probability of a success on one trial, and q denotes the probability of a failure on one trial. 3. The n trials are independent and are repeated using identical conditions.

Answer 55

Expected arithmetic average when an experiment is repeated many times. The average value of values generated by a chance process

Answer 56

A discrete random variable (RV) that arises from Bernoulli trials; there are a fixed number, n, of independent trials. “Independent” means that the result of any trial (for example, trial one) does not affect the results of the following trials, and all trials are conducted under the same conditions. Under these circumstances the binomial RV X is defined as the number of successes in n trials. The notation is: X equiv B(n,p)

Answer 57

A discrete random variable (RV) that arises from the Bernoulli trials; the trials are repeated until the first success. The geometric variable X is defined as the number of trials until the first success.

Answer 58

A statistical experiment with the following properties: 1. There are one or more Bernoulli trials with all failures except the last one, which is a success. 2. In theory, the number of trials could go on forever. There must be at least one trial. 3. The probability, p, of a success and the probability, q, of a failure do not change from trial to trial.

Answer 59

A statistical experiment with the following properties: 1. You take samples from two groups. 2. You are concerned with a group of interest, called the first group. 3. You sample without replacement from the combined groups. 4. Each pick is not independent, since sampling is without replacement. 5. You are not dealing with Bernoulli Trials.

Answer 60

A discrete random variable (RV) that is characterized by: 1. A fixed number of trials. 2. The probability of success is not the same from trial to trial. We sample from two groups of items when we are interested in only one group. X is defined as the number of successes out of the total number of items chosen.

Answer 61

A mathematical description of a discrete random variable (RV), given either in the form of an equation (formula) or in the form of a table listing all the possible outcomes of an experiment and the probability associated with each outcome.

Answer 62

A discrete random variable (RV) that counts the number of times a certain event will occur in a specific interval; characteristics of the variable: 1. The probability that the event occurs in a given interval is the same for all intervals. 2. The events occur with a known mean and independently of the time since the last event. The Poisson distribution is often used to approximate the binomial distribution, when n is “large” and p is “small” (a general rule is that n should be greater than or equal to 20 and p should be less than or equal to 0.05).

Answer 63

A characteristic of interest in a population being studied; common notation for variables are upper case Latin letters X, Y, Z,...; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin letters x, y, and z. For example, if X is the number of children in a family, then x represents a specific integer 0, 1, 2, 3,.... Variables in statistics differ from variables in intermediate algebra in the two following ways. 1. The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if X = hair color then the domain is {black, blond, gray, green, orange}. 2. We can tell what specific value x the random variable X takes only after performing the experiment.

Answer 64

Sample mean approaches population mean as sample size increases. As the number of trials in a probability experiment increases, the difference between the theoretical probability of an event and the relative frequency probability approaches zero.

Answer 65

The decay parameter describes the rate at which probabilities decay to zero for increasing values of x.

Answer 66

A continuous random variable (RV) that appears when we are interested in the intervals of time between some random events, for example, the length of time between emergency arrivals at a hospital;

Answer 67

For an exponential random variable X, the memoryless property is the statement that knowledge of what has occurred in the past has no effect on future probabilities.

Answer 68

If there is a known average of λ events occurring per unit time, and these events are independent of each other, then the number of events X occurring in one unit of time has the Poisson distribution.

Answer 69

A discrete or continuous random variable (RV) that has equally likely outcomes over the domain, a < x < b.

Answer 70

aka the Gaussian distribution; Visualized as a symmetrical bell-shaped curve. The most frequent values cluster around the center, and the probability of finding values far away from the center tapers off gradually in both directions.

Answer 71

A normal distribution with mean 0 and standard deviation of 1

Answer 72

Statistical value that describes a specific data point's relative position within a standard normal distribution (aka Z-Distribution). It tells you how many standard deviations a particular point is away from the mean (average) of the data, expressed in standard deviation units.

Answer 73

The sampling distribution of mean for a variable approximates a normal distribution with increasing sample size. Given a random variable (RV) with known mean μ, known standard deviation σ and known sample size of n - if n is sufficiently large, then the distribution of the sample means and the distribution of the sample sums will approximate a normal distributions regardless of the shape of the population. The mean of the sample means will equal the population mean, and the mean of the sample sums will equal n times the population mean. As sample size, n, increases, the standard deviation of the sampling distribution becomes smaller and because the square root of the sample size is in the denominator. In other words, the sampling distribution clusters more tightly around the mean as sample size increases. Why is it important? 1. Normality Assumption Allows us to use hypothesis test that rely on data that is normally distributed when we have nonnormally distributed data 2. Precision of Estimates We can make our estimate more precise by increasing or sample size

Answer 74

Describes the probability distribution of all possible means you could get if you draw multiple random samples of size n from a population. Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution.

Answer 75

The standard deviation of the distribution of the sample means around the population mean.

Answer 76

A discrete random variable (RV) which arises from Bernoulli trials; there are a fixed number, n, of independent trials. “Independent” means that the result of any trial (for example, trial 1) does not affect the results of the following trials, and all trials are conducted under the same conditions. Under these circumstances the binomial RV X is defined as the number of successes in n trials.

Answer 77

An interval estimate for an unknown population parameter. This depends on: 1, the desired confidence level, 2. information that is known about the distribution (for example, known standard deviation), 3. the sample and its size.

Answer 78

The percent expression for the probability that the confidence interval contains the true population parameter; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Confidence Level = 1- Alpha(α)

Answer 79

The number of objects in a sample that are free to vary. Usually, df = n -1

Answer 80

The margin of error; depends on the confidence level, sample size, and known or estimated population standard deviation.

Answer 81

Also called statistical inference or inductive statistics; this facet of statistics deals with estimating a population parameter based on a sample statistic. For example, if four out of the 100 calculators sampled are defective we might infer that four percent of the production is defective.

Answer 82

A single number computed from a sample and used to estimate a population parameter

Answer 83

Investigated and reported by William S. Gossett in 1908 and published under the pseudonym Student; the major characteristics of the random variable (RV) are: 1. It is continuous and assumes any real values. 2. The pdf is symmetrical about its mean of zero. However, it is more spread out and flatter at the apex than the normal distribution. 3. It approaches the standard normal distribution as n get larger. (n>=30 closely follows normal distribution) 4. There is a "family" of t–distributions: each representative of the family is completely defined by the number of degrees of freedom, which is one less than the number of data.

Answer 84

A statement about the value of a population parameter, in case of two hypotheses, the statement assumed to be true is called the null hypothesis (notation H0) and the contradictory statement is called the alternative hypothesis (notation Ha).

Answer 85

Statistical analysis that uses sample data to assess two mutually exclusive theories about the properties of a population. Based on sample evidence, a procedure for determining whether the hypothesis stated is a reasonable statement and should not be rejected or is unreasonable and should be rejected. 1. Understand Sampling Distribution 2. Understand test statistic given sampling distribution 3. Run Test and receive p-value 4. Evaluate statistical significance and decision Work by taking the observed test statistic from a sample and using the sampling distribution to calculate the probability of obtaining that test statistic if the null hypothesis is correct.

Answer 86

Probability of a Type I error (reject the null hypothesis when it is true). Notation: α. In hypothesis testing, the Level of Significance is called the preconceived α or the preset α. Q: Is this true? See Hypothesis Testing by Jim Frost.

Answer 87

The probability that an event will happen purely by chance assuming the null hypothesis is true. The smaller the p-value, the stronger the evidence is against the null hypothesis. Probability of observing a sample statistic that is at least as extreme as our sample statistic when we assume that the null hypothesis is correct Indicates the strength of the sample evidence against the null hypothesis. Probability we would obtain the observed effect, or larger, if the null hypothesis is correct. If the p-value is less than or equal to the significance level, you reject the null hypothesis, in favor of your alternative hypothesis, and our results are statistically significant. - When the p-value is low, the null must go - If the p-value is high, the null will fly Whenever we see a p-value, we know we are looking at the results of a hypothesis test. Determines statistical significance for a hypothesis test P-values are NOT an error rate! The chance of getting a test statistic assuming the null hypothesis is true. Not the chance of the null hypothesis being correct.

Answer 88

Alpha (α) The decision is to reject the null hypothesis when, in fact, the null hypothesis is true. Ex. Saying there is a change when there is not Ex. Fire alarm going off when there is no fire

Answer 89

Beta (β) The decision is not to reject the null hypothesis when, in fact, the null hypothesis is false. Ex. Saying there is not a change when there is. Ex. Fire alarm does NOT ring when there is a fire

Answer 90

Describes/Summarizes a dataset for a particular group of objects, observations, or people. No attempt to generalize beyond the set of observations.

Answer 91

Science concerned with collecting, organizing, analyzing, interpreting, and presenting data. It equips us with the tools and methods to extract meaningful insights from information.

Answer 92

A distribution that has multiple peaks

Answer 93

1. Central Tendency 2. Spread/Dispersion 3. Correlation/Dependency 4. Shape of Distribution

Answer 94

aka the Median of the data. Splits the entire ordered dataset into 2 equal parts

Answer 95

The value that is the median of the of the upper half of the ordered data set

Answer 96

Measure of the center point or typical value of a dataset

Answer 97

Measure of the amount of dispersion in a dataset. How spread out the values in the dataset are.

Answer 98

The difference between the MAX and MIN value in a dataset.

Answer 99

Situation where two variables appear to have an association, but in reality, a third factor (confounding/lurking variable) causes that association.

Answer 100

Mathematical function that describes the probabilities for all possible outcomes of a random variable

Answer 101

Indicates how much one variable changes (dependent variable) in value in response to change in another variable (independent variable). Value between 0 and 1. Strength of association between 2 variables. Strength: - 1 = perfect relationship - 0.8 = strong - 0.6 = moderate - 0.4 = weak - 0 = no relationship Direction: - Positive = upward slope - Negative = downward slope

Answer 102

Probability distributions for discrete data (assume a set of distinct values)

Answer 103

Probability distribution for continuous data (assumes infinite number of values between any two values)

Answer 104

Discrete probability distribution used to calculate the number of trials that are required to observe an event a specific number of times. In other words, given a known probability of an event occurring and the number of events that we specify, this distribution calculates the probability for observing that number of events within N trials.

Answer 105

Can be used to determine the proportion of values that fall within a specific number of standard deviations from the mean for data that is normally distributed. STDDEV | PERCENTAGE OF DATA 1 | 68% 2 | 95% 3 | 99.7%

Answer 106

Data transformation that creates a standard normal distribution (Z-distribution) with a mean of 0 and standard deviation of 1. Allows for easier comparison between features with different scales.

Answer 107

Data transformation that rescales the data to a specific range, often between 0 and 1 or -1 and 1 (min-max normalization). Ensures that all features are on a similar scale, preventing features with larger ranges from dominating the model during training.

Answer 108

1. Hypothesis Tests 2. Confidence Intervals 3. Regression Analysis

Answer 109

1. Simple Random Sampling 2. Stratified Sampling 3. Cluster Sampling

Answer 110

Variables that we include in the experiment to explain or predict changes in the dependent/response variable.

Answer 111

Variable in the experiment that we want to explain or predict. Values of this variable are dependent on other variables

Answer 112

One event (cause) brings about another event (affect)

Answer 113

Branch of statistics that assumes sample data come from populations that are adequately represented in modeled by probability distributions with a set of parameters.

Answer 114

Branch of statistics that does not assume sample data comes from populations that are adequately represented in modeled by probability distributions with a set of parameters.

Answer 115

H0; One of the two mutually exclusive theories about the population's properties. Typically states that there is no effect.

Answer 116

HA; The other of the two mutually exclusive theories about the population's properties. Typically states that the population parameter does not equal the null hypothesis value. In other words, there is a non-zero effect.

Answer 117

The difference between the population value and the null hypothesis value. Represents the 'signal' in the data

Answer 118

Defines how strong the sample evidence must be to conclude an effect exists in the population. Evidentiary standard set before study begins. Specifies how strongly the sample evidence must contradict the null hypothesis before we can reject the null hypothesis. Standard defined by the probability of rejecting a true null hypothesis. In other words, the probability that we say there is an effect when there is no effect. Evidentiary standard set to determine whether our sample is strong enough to reject the null hypothesis. Confidence Level = 1 - Alpha(α)

Answer 119

Defines sample values on the sampling distribution that are improbable enough to warrant rejecting the null hypothesis and therefore represent statistically significant results.

Answer 120

Type of hypothesis test for the mean and uses the Student's t-distribution sampling distribution and t-value to determine statistical significance

Answer 121

Test statistic for t-test hypothesis test. Used alongside Student's t-Distribution

Answer 122

Hypothesis test where we examine a single population and compare it to a base, hypothesized value. Null: The population mean equals the hypothesized mean Alternative: The population mean does not equal the hypothesized mean Assumptions: 1. Representative, random sample 2. Continuous Data 3. Sample data is normally distributed or Sample Size >= 20

Answer 123

aka nondirectional or two-sided test because we are testing for effects in both directions. When we perform a two-tailed test, we split the significance level percentage between both tails of the distribution. Null: The effect equals zero Alternative: The effect does not equal zero (nothing about direction) We can detect both positive and negative results. Standard in scientific research where discovering ANY type of effect is usually of interest to researchers. Default choice

Answer 124

aka directional or one-sided test because we can test for effects in ONLY one direction. When we perform a one-tailed test, the entire significance level percentage goes into one tail of the distribution. Null: The effect is less than or equal to 0 Alternative: the effect is greater than zero One-tailed tests have more statistical power to detect an effect in one direction than a two-tailed test with the same design and significance level. One-tailed tests occur most frequently for studies where one of the following is true: 1. Effects can exist in only one direction 2. Effects can exist in both directions but we only care about an effect in one direction

Answer 125

Hypothesis test where we examine two populations and compare them to each other. Null: The means for the two populations are equal Alternative: The means for the two populations are not equal Assumptions: 1. Representative, random sample 2. Continuous Data 3. Sample data is normally distributed or each groups size >= 15 4. Groups are independent 5a. Groups have equal variances 5b. Groups have unequal variances --> Use Welch's t-test

Answer 126

Hypothesis test where we assess dependent samples, which are two measurements on the same person or item. Paired t-Test is a 1-Sample t-test where our hypothesized value 0 effect for the difference between the pre- and the post-observations. Null: The difference between pre- and post-observations are equal Alternative: The difference between pre- and post-observations are not equal Assumptions: 1. Representative, random sample 2. Independent observations 3. Continuous data 4. Data is normally distributed or sample size >= 20

Answer 127

If our test fails to detect an effect, that's not proof it doesn't exist. It just means our sample contains an insufficient amount of evidence to conclude that an effect exists. Lack of proof doesn't represent proof that something doesn't exist

Answer 128

A value that hypothesis tests calculate from our sample data. This value boils our data down into a single number, which measures the overall DIFFERENCE between our sample data and our null hypothesis. Represents the signal-to-noise ratio for a particular sample = signal/noise Measures the difference between the data and what is expected by the null hypothesis Ex. (hypothesis test, test statistics) = (t-test, t-value)

Answer 129

Hypothesis Test's ability to detect an effect that actually exists. Test correctly rejects the a false null hypothesis. 80% is the standard benchmark for studies Power = 1 - Beta(β) = Opposite of Type II errors Beta(β) = Type II Error Factors that affect power: 1. Sample Size - Larger = higher power 2. Variability - Lower = higher power 3. Effect Size - Larger = higher power

Answer 130

To assess whether a data set fits a specific distribution, we can apply the goodness-of-fit hypothesis test that uses the chi-square distribution. Null hypothesis states that the data comes from the assumed distribution. Test compares observed values against the values you would expect to have if the data followed the assumed distribution. Test is right-tailed. Each observation or cell category must have an expected value of at least 5.

Answer 131

To assess whether two factors are independent, we can apply the test of independence that uses the chi-square distribution. Null hypothesis states that the two factors are independent. Test compares observed values to expected values. Test is right-tailed. Each observation or cell category must have an expected value of at least 5.

Answer 132

To assess whether two datasets are derived from the same distribution, which can be unknown, we can apply the test of homogeneity that uses the chi-square distribution. Null hypothesis states that the populations of the two data sets come from the same distribution. Test compares the observed values against the expected values if the two populations followed the same distribution. Test is right-tailed. Each observation or cell category must have an expected value of at least 5.

Answer 133

Hypothesis test used if you know the population standard deviation (companion of the t-test which is used when you only have an estimate of the population standard deviation) Argument by contradiction, designed to show that the null hypothesis will lead to an absurd conclusion and must therefore be rejected.

Answer 134

Indicates that our sample provides enough evidence to conclude that the effect exists in the population (via p-value). Factors that influence statistical significance: 1. Effect Size 2. Sample Size 3. Variability

Answer 135

Asking whether a statistically significant effect is substantial enough to be meaningful.

Answer 136

Managing the tradeoffs between effect size, sample size, and variability to settle on a sample size needed for a hypothesis test. Our goal is to collect a large enough sample to have sufficient power to detect a meaningful effect but not too large to be wasteful.

Answer 137

y = mx+b y = dependent variable m = slope x = independent variable b = y-intercept

Answer 138

Tells us how much the dependent variable (y) changes for every one unit increase in the independent variable (x), on average.

Answer 139

Used to describe the dependent variable when independent variable equals zero.

Answer 140

Measures the strength of the linear relationship between x and y. Value between -1 and 1

Answer 141

Equal to the square of the correlation coefficient, r. When expressed as a percent, r^2 represents the percent of variation in the dependent variable, y, that can be explained by variation in the independent variable x using the regression line.

Answer 142

1. Linear 2. Independent 3. Normal 4. Equal Variance 5. Random TODO - expand

Answer 143

Method of testing whether of note the means of three or more populations are equal TODO - expand

Answer 144

Hypothesis test that allows us to compare more group means (3 or more). Requires one categorical factor for the independent variable and a continuous variable for the dependent variable. The values of the categorical factor divide the continuous data into groups. The test determines whether the mean differences between these groups is statistically significant. Null: All group means are equal (F-value = 1) Alternative: Not all group means are equal (F-value != 1) Assumptions: 1. Random Samples 2. Independent Groups 3. Dependent variable is continuous 4. Independent variable is categorical 5. Sample data is normally distributed or each group has 15 or more observations 6. Group should have roughly equal variances or use Welch's ANOVA

Answer 145

Used to assess differences between group means that are defined by two categorical factors. More closely resembles Linear Regression. (Just use linear regression) Assumptions: 1. Dependent variable is continuous 2. The 2 independent variables are categorical 3. Random residuals with constant variance

Answer 146

Distributed used in an F-test. TODO

Answer 147

Test statistic used in an F-test alongside an F-Distribution. Ratio of two variances, or technically, two mean squares.

Answer 148

Type of hypothesis test for the mean and uses the F-distribution sampling distribution and F-statistic to determine statistical significance

Answer 149

Used to explore difference between multiple group means while controlling the experiment-wise error rate as ANOVA will only tell us IF there exist a difference between ANY of the group means. Types: - Tukey's Method - Dunnett's Method - Hsu's MCB

Answer 150

similar, treatment

Answer 151

eligible, unbiased

Answer 152

Patients that were part of a control group in the past. These observations are not contemporaneous with the current treatment group

Answer 153

Fundamental statistical method where we can understand the effect of a treatment by establishing a CONTROL and TREATMENT group where the "only" difference is the treatment. Any difference between then between these two groups is associated with/caused by with the treatment. Caution: Confounding variables

Answer 154

There is a test and control group in the experiment, but the members of the groups are not randomly assigned from an eligible group.

Answer 155

Experiment where members of control and treatment group are randomly drawn from an "eligible" group

Answer 156

Control groups that are drawn at the same time as the treatment group. Opposite of "Historical Controls".

Answer 157

A study where researchers do not assign experimental units into the treatment and control groups but rather observe experimental units that assign themselves to the different groups. Some subjects have the condition whose effects are being studied; this is the treatment group. The other subjects are the controls. Can only establish association.

Answer 158

A formal relationship between two variables measured by correlation. Circumstantial evidence for causation.

Answer 159

Association = two variables (X, Y) have a correlation. When one variable moves, another moves predictably. Unknown if variable X causes the move in Y or not, we just know Y responses predictably. Causation = same as association but we have performed a randomized-controlled experiment to confirm causation. X causes the move in Y.

Answer 160

A statistical phenomenon where a trend appears in one set of data but disappears or reverses when the data is aggregated. This can occur when there is a confounding variable that distorts the relationship between the variables of interest. Ex. Admissions rates between men and women at UC Berkeley

Answer 161

A table that shows the percentage of data found in each class interval

Answer 162

Y-axis on a histogram representing "percent per" horizontal unit Ex. Percent per Thousand Dollars

Answer 163

Percent Interval 100

Answer 164

Measures how big the entries of a list are, neglecting signs rms size of a list = sqrt(avg(entries^2)) Name in reverse to perform rms: 1. SQUARE Entires 2. Take their MEAN 3. ROOT the average

Answer 165

Average is not good if the list entries are both positive AND negative because the positives and the negatives can cancel each other out leaving the average value around 0. rms gets around this problem by squaring all entries first

Answer 166

rms average

Answer 167

Study where subjects are compared to each other at one point in time

Answer 168

Study where subjects are compared to themselves at different points in time

Answer 169

Cross-Sectional compares many subjects at the same time and longitudinal looks at the same subjects but over many periods of time.

Answer 170

Median Average

Answer 171

Percentiles

Answer 172

0. Does not change.

Answer 173

When you change from one unit to another by performing a constant operation on all entries in a list

Answer 174

Chance Error

Answer 175

Chance Error

Answer 176

Refers to the random fluctuations that occur in data due to sampling variability. The likely size of this value being the SD of a sequence of repeated measurements made under the same conditions. For a chance model, the chance error is measured by the standard error

Answer 177

Occurs when the value obtained from a measurement differs from the true value of the quantity being measured. This error can arise due to various factors, including chance error and systematic error (or bias)

Answer 178

Bias Chance Error

Answer 179

Bias Chance Error

Answer 180

Rise/Run The rate at which y increases with x

Answer 181

The height of the line (y-value) at x=0. The x-value of the line when it intersects with the y-axis.

Answer 182

Strong Weak

Answer 183

The dot on a scatter plot that represents a value with (x-average, y-average)

Answer 184

1. Average of x-values 2. SD of x-values 3. Average of y-values 4. SD of y-values 5. Correlation (r)

Answer 185

r = avg( (x in standard units) * (y in standard units) ) Convert each variable to standard units and then take the average product Measurement of LINEAR association between two variables.

Answer 186

Line on scatter plot that goes through all (x,y) points that are equal number of SDs away from the average, for both variables Will pass through point of Averages (x=0 SD, y = 0 SD) slope = (SD of y)/(SD of x)

Answer 187

Subtract mean from value and then divide by the standard deviation. z = ( x - avg ) / SD

Answer 188

Interchanging Adding Multiplying

Answer 189

Standard Deviations

Answer 190

Linear In General

Answer 191

Technique that models the relationship between a dependent variable and one or more independent variables. Way of using the correlation coefficient to estimate the average value of y for each value of x Associated with each increase of one SD in x, there is an increase of r * SDs in y, on average

Answer 192

Estimates the average value of y for a corresponding value of x

Answer 193

In virtually all test-retest situations, the bottom group on the first test will, on average, show some improvement on the second test and the top group will, on average, fall back.

Answer 194

Thinking that the Regression Effect is due to something important and not just spread around the regression line

Answer 195

The distance of the predicted value from the actual value. Error = actual - predicted

Answer 196

Tells you how much error you can expect from your predictions vs the actual, on average. Measures spread around the regression line in absolute terms

Answer 197

Being predicted

Answer 198

Among all lines, the one that makes the smallest rms error in prediction y from x The regression line that minimizes the rms error the most aka the regression line

Answer 199

The process of getting least squares estimates until you generate the least squares line

Answer 200

Slope and intercept of a regression line. The ones that minimize the rms the most become the least squares line

Answer 201

To find the chance that AT LEAST ONE OF TWO things will happen, check to see if they are mutually exclusive. If they are, add the chances.

Answer 202

The chance that two independent events will both happen equals the chance that the first will happen, multiplied by the chance that the second will happen given the first has happened.

Answer 203

Independent says that the probability of event A is not affected by event B while mutually exclusive is the exact opposite where the event B makes event A chance equal 0.

Answer 204

Do not Too Big

Answer 205

Refers to the random fluctuations that occur in data due to sampling or measurement errors. It's the inherent uncertainty that exists in any data set, even when collected and analyzed carefully.

Answer 206

A model that can assist in modeling a population You have a box with a series of tickets in it that you are drawing at random. An operation is then performed on the draws (sum, average, etc.)

Answer 207

Standard Deviation = rms of value deviations from the average Standard Error = difference between the sample average and the expected value (population average)

Answer 208

Principle that states that the standard error of a sample proportion, or mean, decreases in proportion to the square root of the sample size. In simpler terms, this means that as you increase the sample size, the accuracy of your estimate (whether it's a proportion or a mean) improves, but not at a linear rate. Instead, the improvement gets smaller and smaller as the sample size gets larger. Part of a formula used to compute the SE for a sum of draws made at random with replacement (independent) from a box. The square root law is the mathematical explanation for the law of averages.

Answer 209

= number of draws * avg of box

Answer 210

= expected value + chance error In general, the sum is likely to be around its expected value, give or take the chance error (measured with standard error)

Answer 211

How big is the chance error around the expected value of the sum likely to be? = sqrt(num draws) * SD_of_box Each draw adds some extra variability to the sum, because you don't know how it is going to turn out. As the number of draws goes up, the sum gets harder to predict, the chance error (absolute) gets bigger, and so does the standard error Here we can see the square root law in effect

Answer 212

Expected value for the sum Standard Error for the sum

Answer 213

Values that are returned by the chance process/ box model = expected value + chance error

Answer 214

Number Standard Deviation (SD) Expected Value (of sum) (EV) Standard Error (of sum) (SE) -

Answer 215

Instead of the chance process producing a value between A and B, it will produce either a 0 or a 1. Our same formulas from before can be used.

Answer 216

normal curve 30 observations

Answer 217

A new king of graph that represents chance rather than data. Each rectangle represents the chance of a given interval occurring. Sums to 100%. x-Axis = Sum of Box Model y-Axis = Percent per standard unit With enough draws, the probability histogram for the sum will be close to the normal curve

Answer 218

Experimentally Observed

Answer 219

Gets closer and closer to

Answer 220

Normal Curve

Answer 221

The systematic tendency on the part of the sampling procedure to execute one kind of person or another from the sample. Taking a larger sample does not help this problem, it just repeats the basic mistake on a larger scale

Answer 222

Bias for members of the sample to be people that respond rather than all members selected to be in the sample initially Non-respondents can be very different from respondents.

Answer 223

Sampling members of a population until the desired sample size is met

Answer 224

Population Percentage

Answer 225

= (SE for # / Size of sample)*100% First get the SE for the corresponding responding number; then convert to percentage, relative to the size of the sample

Answer 226

Square Root

Answer 227

Up Square Root

Answer 228

Down Square Root

Answer 229

Expected Value SE for the Sample Percentage

Answer 230

SD = sqrt( p * (p-1) ) SD = sqrt(percentage of 1s * percentage of 0s)

Answer 231

Absolute Size Size Relative

Answer 232

Population Size Absolute Size of the Sample Standard Error (via SD) (20.4)

Answer 233

= Sample Percentage +- N SE's

Answer 234

Confidence Interval

Answer 235

Probabilities Confidence levels

Answer 236

Population Percentage Standard Error (SE)

Answer 237

Sample Population

Answer 238

Confidence Interval SEs Confidence Level

Answer 239

= Average of Box

Answer 240

= SE for sum / # of draws Tells you how far off the Expected Value of the Sample Average is from the population average

Answer 241

- The SD says how far values are from the average - on average - The SE says how far sample average are from the population average - on average

Answer 242

Because with sample random sampling, we assume that the chance error is normally distributed around the observed value.

Answer 243

Sum of 1s / # of draws

Answer 244

SE for sum, from a 0-1 box

Answer 245

Sum of 1s / # of draws

Answer 246

= (SE for count / # of draws)*100%

Answer 247

SD Confidence Interval Confidence Level

Answer 248

A randomized-controlled double/triple blind experiment

Answer 249

Standard Deviation = rms of deviations from average

Answer 250

We can estimate it using the SD of a sequence of repeated measurements made under the same conditions

Answer 251

More precise than any individual estimate, by a factor equal to the square root of the number of measurements.

Answer 252

Because the first step to calculating it is to convert to standard units

Answer 253

We can run tests of significance to understand how likely our results are given the assumption of "no effect" (null hypothesis)

Answer 254

Null Hypothesis Alternative Hypothesis

Answer 255

Chance of getting a test statistic as extreme as, or more extreme than, the observed one. The chance is computed on the basis that the null hypothesis is true. The small this chance is, the stronger the evidence against the null.

Answer 256

Procedure used to determine whether an observed effect or difference is statistically significant or due to chance. It helps us decide if our findings are meaningful or if they could have occurred by chance. Steps: 1. Setup Null & Alternative Hypothesis 2. Pick a test statistic, to measure the difference between the observed data and what is expected by the null hypothesis. 3. Compute the observed significance level P

Answer 257

- Compute EV and SE for each average independently -

Answer 258

= sqrt(a^2 + b^2) a = SE for average_A b = SE for average_B

Answer 259

1. the sizes of the two samples 2. the averages of the two samples 3. the SDs of the two samples Assumes two independent random samples

Answer 260

= EV_A - EV_B

Answer 261

Statistical hypothesis test used to determine if there is a significant difference between observed and expected frequencies in one or more categories. It's commonly used to analyze categorical data. a) Categorical Data b) Chance model c) Frequency Table d) X^2 Statistic e) Degrees of Freedom f) Observed Significance Level (P)

Answer 262

sum of ( (observed freq. - expected freq)^2 / expected freq. )

Answer 263

Sample Size Large Small

Statistics Flashcards

- OpenStax Introductory Statistics - Introduction to Statistics 4E, Freedman