Terms : Hide Images
| 13822744420 | Interpret Standard Deviation | Standard Deviation measures spread by giving the "typical" or "average" distance that the observations (context) are away from their (context) mean | 0 | |
| 13822748429 | Linear Transformations | Adding "a" to every member of a data set adds "a" to the measures of position, but does not change the measures of spread or the shape. Multiplying every member of a data set by "b" multiplies the measures of position by "b" and multiplies most measures of spread by |b|, but does not change the shape. | 1 | |
| 13822752482 | SOCS | Shape - Skewed Left (Mean < Median) Skewed Right (Mean > Median) Fairly Symmetric (MeanMedian) Outliers - Discuss them if there are obvious ones Center- Mean or Median Spread- Range, IQR, or Standard Deviation Note: Also be on the lookout for gaps, clusters or other unusual features of the data set. Make Observations! | 2 | |
| 13822775428 | Interpret a z-score | z = (value - mean) / standard deviation A z-score describes how many standard deviations a value falls away from the mean of the distribution and in what direction. The further the z-score is away from zero the more "surprising" the value of the statistic is. | 3 | |
| 13822791413 | Interpret LSRL Slope "b" | For every one unit change in the x variable (context) the y variable (context) is predicted to increase/decrease by ____ units (context). | 4 | |
| 13822805485 | Outlier Rule | Upper Bound = Q3 + 1.5(IQR) Lower Bound = Q1 - 1.5(IQR) IQR = Q3 - Q1 | 5 | |
| 13822814672 | Describe the Distribution OR Compare the Distributions | SOCS! Shape, Outliers, Center, Spread Only discuss outliers if there are obviously outliers present. Be sure to address SCS in context! If it says "Compare" YOU MUST USE comparison phrases like "is greater than" or "is less than" for Center & Spread | 6 | |
| 13822822878 | Using Normalcdf and Invnorm (Calculator Tips) | Normalcdf (min, max, mean, standard deviation) Invnorm (area to the left as a decimal, mean, standard deviation) | 7 | |
| 13822828404 | What is an outlier? | When given 1 variable data: An outlier is any value that falls more than 1.5(IQR) above Q3 or below Q1 Regression Outlier: Any value that falls outside the pattern of the rest of the data. | 8 | |
| 13822843577 | Interpret LSRL y-intercept "a" | When the x variable (context) is zero, the y variable (context) is estimated to be put value here. | 9 | |
| 13822850164 | Interpret r-squared | __% of the variation in y (context) is accounted for by the LSRL of y (context) on x (context) OR ___% of the variation in y (context) is accounted for by using the linear aggression model with x (context) as the explanatory variable. | 10 | |
| 13822850165 | Interpret r | Correlation measures the strength and direction of the linear relationship between x and y. r is always between -1 and 1. Close to zero = very weak, Close to 1 or -1 = stronger Exactly 1 or -1 = perfectly straight line Positive r = positive correlation Negative r = negative correlation | 11 | |
| 13822857233 | Interpret LSRL "SEb" | SEb measures the standard deviation of the estimated slope for predicting the y variable (context) from the x variable (context). SEb measures how far the estimated slope will be from the true slope, on average. | 12 | |
| 13822860277 | Interpret LSRL "s" | s = ___ is the standard deviation of the residuals. It measures the typical distance between the actual y-values (context) and their predicted y-values (context) | 13 | |
| 13822862635 | Interpret LSRL "y-hat" | y-hat is the "estimated" or "predicted" y-value (context) for a given x-value (context) | 14 | |
| 13822876803 | Interpreting a Residual Plot | 1. Is there a curved pattern? If so, a linear model may not be appropriate. 2. Are the residuals small in size? If so, predictions using the linear model will be fairly precise. 3. Is there increasing (or decreasing) spread? If so, predictions for larger (smaller) values of x will be more variable. | 15 | |
| 13822882496 | What is a residual? | Residual = y - y-hat A residual measures the difference between the actual (observed) y-value in a scatterplot and the y-value that is predicted by the LSRL using its corresponding x value. | 16 | |
| 13822884849 | Sampling Techniques | 1. SRS- Number the entire population, draw numbers from a hat (every set of n individuals has equal chance of selection) 2. Stratified - Split the population into homogeneous groups, select an SRS from each group. 3. Cluster - Split the population into heterogeneous groups called clusters, and randomly select whole clusters for the sample. Ex. Choosing a carton of eggs actually chooses a cluster (group) of 12 eggs. 4. Census - An attempt to reach the entire population 5. Convenience- Selects individuals easiest to reach 6. Voluntary Response - People choose themselves by responding to a general appeal. | 17 | |
| 13822911612 | Experimental Designs | 1. CRD (Completely Randomized Design) - All experimental units are allocated at random among all treatments 2. RBD (Randomized Block Design) - Experimental units are put into homogeneous blocks. The random assignment of the units to the treatments is carried out separately within each block. 3. Matched Pairs - A form of blocking in which each subject receives both treatments in a random order or the subjects are matched in pairs as closely as possible and one subject in each pair receives each treatment, determined at random. | 18 | |
| 13822921422 | Goal of Blocking Benefit of Blocking | The goal of blocking is to create groups of homogeneous experimental units. The benefit of blocking is the reduction of the effect of variation within the experimental units. (context) | 19 | |
| 13822964144 | Advantage of using a Stratified Random Sample Over an SRS | Stratified random sampling guarantees that each of the strata will be represented. When strata are chosen properly, a stratified random sample will produce better (less variable/more precise) information than an SRS of the same size. | 20 | |
| 13822978549 | Experiment or Observational Study? | A study is an experiment ONLY if researchers IMPOSE a treatment upon the experimental units. In an observational study researchers make no attempt to influence the results. | 21 | |
| 13822981337 | Does A cause B? | Association is NOT Causation! An observed association, no matter how strong, is not evidence of causation. Only a well-designed, controlled experiment can lead to conclusions of cause and effect. | 22 | |
| 13822990258 | SRS | A simple random sample of sample size is a sample in which each set of elements in the population has an equal chance of selection. | 23 | |
| 13824507267 | P (at least one) | 1-P(none) | 24 | |
| 13824511433 | complementary events | Two or more mutually exclusive events that together cover all possible outcomes. The sum of the probabilities of complementary events is 1. Ex: Rain/Not Rain, Draw at least one heart I Draw NO hearts | 25 | |
| 13824522167 | Why use a control group? | A control group gives the researchers a comparison group to be used to evaluate the effectiveness of the treatment(s). (context) (gauge the effect of the treatment compared to no treatment at all) | 26 | |
| 13824538785 | Two Events are Independent If... | P(B) = P(B|A) Or P(B) = P(B|Ac) Meaning: Knowing that Event A has occurred (or not occurred) doesn't change the probability that event B occurs. | 27 | |
| 13824545473 | Interpreting Probability | The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions. Probability is a long-term relative frequency. | 28 | |
| 13824551079 | Interpreting Expected Value/Mean | The mean/expected value of a random variable is the long-run average outcome of a random phenomenon carried out a very large number of times. | 29 | |
| 13824579586 | Mean and Standard Deviation of a Discrete Random Variable (On formula page) | Mean (Expected Value): Multiply & add across the table Standard Deviation: Square root of the sum of (Each x value - the mean)^2*(its probability) | 30 | |
| 13824605252 | Mean and Standard Deviation of a Difference of Two Random Variables |  | 31 | |
| 13824626124 | Mean and Standard Deviation of a Sum of Two Random Variables |  | 32 | |
| 13824635155 | Binomial Distribution (Conditions) | 1. Binary? Trials can be classified as success/failure 2. Independent? Trials must be independent. 3. Number? The number of trials (n) must be fixed in advance 4. Success? The probability of success (p) must be the same for each trial. | 33 | |
| 13824639842 | Geometric Distribution (Conditions) | 1. Binary? Trials can be classified as success/failure 2. Independent? Trials must be independent. 3. Trials? The goal is to count the number of trials until the first success occurs 4. Success? The probability of success (p) must be the same for each trial. | 34 | |
| 13824643409 | Binomial Distribution (Calculator Usage) | Exactly 5: P(X = 5) = Binompdf(n, p, 5) At Most 5: P(X 5) = Binomcdf(n, p, 5) Less Than 5: P(X < 5) = Binomcdf(n, p, 4) At Least 5: P(X 5) = 1-Binomcdf(n, p, 4) More Than 5: P(X> 5) =1-Binomcdf(n, p, 5) Remember to define X, n, and p! | 35 | |
| 13824771151 | Mean and Standard Deviation Of a Binomial Random Variable |  | 36 | |
| 13824784273 | Why Large Samples Give More Trustworthy Results... (When collected appropriately) | When collected appropriately, large samples yield more precise results than small samples because in a large sample the values of the sample statistic tend to be closer to the true population parameter. | 37 | |
| 13824790962 | The Sampling Distribution of the Sample Mean (Central Limit Theorem) | 1. If the population distribution is Normal the sampling distribution will also be Normal with the same mean as the population. Additionally, as n increases the sampling distribution's standard deviation will decrease 2. If the population distribution is not Normal the sampling distribution will become more and more Normal as n increases. The sampling distribution will have the same mean as the population and as n increases the sampling distribution's standard deviation will decrease. | 38 | |
| 13824795670 | unbiased estimator | The data is collected in such a way that there is no systematic tendency to overestimate or underestimate the true value of the population parameter. (The mean of the sampling distribution equals the true value of the parameter being estimated) | 39 | |
| 13824799130 | Bias | The systematic favoring of certain outcomes due to flawed sample selection, poor question wording, undercoverage, nonresponse, etc. Bias deals with the center of a sampling distribution being "off'! | 40 | |
| 13824805246 | Explain/Interpret a P-value | Assuming that the null is true (context) the P-value measures the chance of observing a statistic (or difference in statistics) (context) as large as or larger than the one actually observed. | 41 | |
| 13824813065 | Can we generalize the results to the population of interest? | Yes, if: A large random sample was taken from the same population we hope to draw conclusions about. | 42 | |
| 13824818475 | Finding the Sample Size (For a given margin of error) |  | 43 | |
| 13824825565 | Carrying out a Two-Sided Test from a Confidence Interval |  | 44 | |
| 13824832502 | 4-Step Process Confidence Intervals | STATE(P): What parameter do you want to estimate, and at what confidence level? PLAN(AN): Choose the appropriate inference method. Check conditions. DO(I): If the conditions are met, perform calculations. CONCLUDE(C): Interpret your interval in the context of the problem. | 45 | |
| 13824845585 | 4-Step Process Significance Tests | STATE (P/H): What hypotheses do you want to test, and what what significance level? Define any parameters you use. PLAN (A/N): Choose the appropriate inference method. Check conditions. DO (T/O): If the conditions are met, perform calculations. Compute the test statistic and find the P-value. CONCLUDE (M/S): Make a decision about the hypotheses in the context of the problem. | 46 | |
| 13824863455 | Interpreting a Confidence Interval (Not a Confidence Level) |  | 47 | |
| 13824867557 | Interpreting a Confidence Level (The Meaning of 95% Confident) |  | 48 | |
| 13824876279 | Paired t-test Phrasing Hints, Ho and Ha, Conclusion |  | 49 | |
| 13824884211 | Two Sample t-test Phrasing Hints, Ho and Ha, Conclusion |  | 50 | |
| 13824891609 | Type I Error, Type II Error, & Power | 1. Type I Error: Rejected H₀ when H₀ is actually true. (ex. Convicting an innocent person) 2. Type II error: Failing to (II) reject H₀ when H₀ should be rejected. (Ex. Letting a guilty person go free) 3. Power: Probability of rejecting H₀ when H₀ should be rejected. (Rejecting Correctly) | 51 | |
| 13824897134 | Factors that Affect Power | 1. Sample Size: To increase power, increase sample size. 2. Increase α: A 5% test of significance will have a greater chance of rejecting the null than a 1% test. 3. Consider an alternative that is farther away from μ0: Values of μ that are in Ha, but lie close to the hypothesized value are harder to detect than values of μ that are far from μ0. | 52 | |
| 13824906238 | Inference for Means (Conditions) | Random: Data from a random sample(s) or randomized experiment Normal: Population distribution is normal or large sample(s) (n1 ≥ 30 or n1 ≥ 30 and n2 ≥ 30) Independent: Independent observations and independent samples/groups; 10% condition if sampling without replacement | 53 | |
| 13824918971 | Inference for Proportions (Conditions) | Random: Data from a random sample(s) or randomized experiment Normal: At least 10 successes and failures (in both groups, for a two sample problem) Independent: Independent observations and independent samples/groups; 10% condition if sampling without replacement | 54 | |
| 13824921733 | Types of Chi-Square Tests | 1. Goodness of Fit: Use to test the distribution of one group or sample as compared to a hypothesized distribution. 2. Homogeneity: Use when you you have a sample from 2 or more independent populations or 2 or more groups in an experiment. Each individual must be classified based upon a single categorical variable. 3. Association/Independence: Use when you have a single sample from a single population. Individuals in the sample are classified by two categorical variables. | 55 | |
| 13824929594 | Chi-Square Tests df and Expected Counts |  | 56 | |
| 13824932611 | Inference for Counts (Chi-Squared Tests) (Conditions) |  | 57 | |
| 13824936968 | Inference for Regression (Conditions) | Linear: True relationship between the variables is linear. Independent observations, 10% condition if sampling without replacement Normal: Responses vary normally around the regression line for all x-values Equal Variance around the regression line for all x-values Random: Data from a random sample or randomized experiment | 58 |
