C1 Intro to Probability and Data Analysis with R M4 Exploratory Data Analysis | Inference Intro Flashcards

Question

Variance

Answer 1

Variance is roughly the average squared deviation from the mean

Answer 2

Standard deviation is the square root of the variance, and standard deviation has the same units as the data. ## Footnote The standard deviation represents the typical deviation of observations from the mean.

Answer 3

Distributions where more observations are clustered around the center, are less variable, versus distributions where more observations are away from the center, are more variable. ## Footnote A set with more data at the ends of the distribution (away from the center) is more variable. Diversity in a set refers to the number of different discrete values, not how far or close to the center of a distribution these values are.

Answer 4

True ## Footnote The statistic mean/median (mean divided by median) can be used as a measure of skewness (either right or left)

Answer 5

An outlier is an observation that appears extreme relative to the rest of the data. ## Footnote Examining data for outliers serves many useful purposes, including 1. Identifying strong skew in the distribution. 2. Identifying possible data collection or data entry errors. 3. Providing insight into interesting properties of the data.

Answer 6

Extending out from the box, the whiskers attempt to capture the data outside of the box. However, their reach is never allowed to be more than 1.5 × IQR. They capture everything within this reach. ## Footnote In a sense, the box is like the body of the box plot and the whiskers are like its arms trying to reach the rest of the data.

Answer 7

True Any observation lying beyond the whiskers is labeled with a dot. ## Footnote The purpose of labeling these points– instead of extending the whiskers to the minimum and maximum observed values– is to help identify any observations that appear to be unusually distant from the rest of the data.

Answer 8

We define robust statistics as measures on which extreme observations have little effect. The median is a more robust statistic of center than the mean. The IQR, which is based on the median, is a more robust statistic than the standard deviation which is calculated using the mean. ## Footnote Robust statistics are most useful for describing skewed distributions, or those with extreme observations. While non-robust statistics like mean and standard deviation are useful for describing symmetric distributions

Answer 9

A transformation is a rescaling of the data using a function. When data are very strongly skewed, we sometimes transform them, so that they are easier to model. ## Footnote We might want to reduce skew to assist in modeling or we might want to straighten a nonlinear relationship in a scatterplot, so that we can model the relationship with simpler methods.

Answer 10

The most commonly used transformation is the natural log transformation, which is often applied when much of the data cluster near zero relative to larger values in the dataset and all observations are positive.

Answer 11

1) We start with a null hypothesis that represents that status quo. 2) We also have an alternative hypothesis that represents our research question, in other words, what we're testing for. 3) We conduct a hypothesis test under the assumption that the null hypothesis is true, either via simulation or using theoretical methods. A: If the test results suggest that the data do not provide convincing evidence for the alternative hypothesis, we stick with the null hypothesis. B:If they do, then we reject the null hypothesis in favor of the alternative.

Answer 12

A contingency table is a type of table used in statistics to display the frequency distribution of two categorical variables. It helps to summarize the relationship between these variables by showing how the categories of one variable relate to the categories of another.

Answer 13

Purpose of a Contingency Table: **Relationship Evaluation**: It allows researchers to evaluate whether there is an association or relationship between the two categorical variables. **Conditional Distribution**: It helps in calculating conditional distributions, which show the distribution of one variable given the levels of the other variable. **Data Visualization**: It provides a clear visual representation of the data, making it easier to identify patterns or trends. **Statistical Analysis**: It serves as a basis for various statistical tests, such as the Chi-square test, to determine if the observed frequencies differ significantly from expected frequencies.

Answer 14

A graphical way of representing data with a single categorical variable is a bar plot. ## Footnote Also, we usually consider the relative frequencies when evaluating the distributions of categorical variables. We can also make a bar plot of these relative frequencies, which look just like the original bar plot but just has the relative frequencies instead of the counts on the y-axis.

Answer 15

First, bar plots are used for displaying distributions of categorical variables, while histograms are used for numerical variables. Second, the axis in a histogram is a number line. Hence, the orders of the bars cannot be changed. While in a bar plot, the categories can be listed in any order, though some orderings make more sense than others, especially for original variables.

Answer 16

A segmented bar plot is useful for visualizing conditional frequency distributions of categorical variables. ## Footnote In other words, the distribution of the levels of one variable, the response variable, conditioned on the levels of the other, the explanatory variable.

Answer 17

True ## Footnote Mosaic plots are useful only for categorical variables.

Answer 18

The probability of observing data under the assumption that the null hypothesis is true, is called the p-value.

Answer 19

It suggests a relationship between categorical variables. ## Footnote 35/290 ≈ 12% of Republicans, 146/341 ≈ 43% of Democrats, and 69/341 ≈ 20% of Independents think that teachers belonging to unions or bargaining associations helped the quality of public school education in the United States. Since there is considerable differences between these proportions, the results of the survey suggest a relationship between opinion on teachers belonging to unions or bargaining associations and political party affiliation.