Week 7: Descriptive Statistics and Confidence Intervals

<p>Bayesian statistics can only be applied to large datasets. (A)</p> Signup and view all the answers

<p>The probability of observing the data assuming a certain belief is true. (A)</p> Signup and view all the answers

<p>It ensures that observed frequencies will converge to the true probability with an increasing number of trials. (B)</p> Signup and view all the answers

<p>Scores become more frequent as they move away from the center. (A)</p> Signup and view all the answers

<p>They result from a large number of small, independent random variables, which tend to cancel each other out. (C)</p> Signup and view all the answers

<p>As sample size increases, the distribution of the sample means will approach a normal distribution. (C)</p> Signup and view all the answers

<p>Long-run frequency of events to interpret probabilities. (A)</p> Signup and view all the answers

<p>Crowd estimates can yield surprisingly accurate predictions even among non-experts. (A)</p> Signup and view all the answers

<p>Normal distribution. (C)</p> Signup and view all the answers

<p>It is an estimate based on sample data that offers the best guess for population parameters. (A)</p> Signup and view all the answers

<p>It remains largely unaffected by extreme values. (C)</p> Signup and view all the answers

<p>All three values are equal. (C)</p> Signup and view all the answers

<p>The top and bottom 25% of the data. (D)</p> Signup and view all the answers

<p>They provide a range of values that may contain the parameter if the experiment is repeated. (A)</p> Signup and view all the answers

<p>More samples can reduce error and increasingly reflect the population value. (A)</p> Signup and view all the answers

<p>Assumptions about normality significantly affect the validity of results. (C)</p> Signup and view all the answers

<p>It can be skewed by extreme values in the dataset. (C)</p> Signup and view all the answers

<p>It aggregates data into bins to show frequency distributions effectively. (B)</p> Signup and view all the answers

<p>It encompasses the mean, median, and mode which describe the center of a distribution. (D)</p> Signup and view all the answers

<p>It is relatively unaffected by extreme values. (C)</p> Signup and view all the answers

<p>To provide a range of values likely containing a population parameter. (D)</p> Signup and view all the answers

<p>It can be dramatically affected by extreme scores. (B)</p> Signup and view all the answers

<p>Smaller samples provide less reliable mean estimates. (B)</p> Signup and view all the answers

<p>Influence of extreme scores on understanding data spread. (A)</p> Signup and view all the answers

<p>Square the differences from the mean and divide by N-1. (B)</p> Signup and view all the answers

<p>Subjective probability (A)</p> Signup and view all the answers

<p>It reflects how far a single value is from the mean in standard deviation units. (B)</p> Signup and view all the answers

<p>The method to divide stakes based on expected value. (D)</p> Signup and view all the answers

<p>Renaissance (A)</p> Signup and view all the answers

<p>It explains that the mean of sample means converges to the population mean as the sample size increases. (C)</p> Signup and view all the answers

<p>The frequency of an event becomes more accurate as the number of trials increases. (B)</p> Signup and view all the answers

<p>The average estimate of a large group can exceed individual expert accuracy. (D)</p> Signup and view all the answers

<p>It is not applicable to complex games or scenarios beyond simple ones. (D)</p> Signup and view all the answers

<p>They provide the basis for many statistical methods and are a synthetic result of large numbers of independent factors. (D)</p> Signup and view all the answers

The weighted average of all possible outcomes, considering their probabilities.

A function showing the likelihood of different outcomes occurring.

A way of viewing probability as the long-run frequency of events, based on repeated observations.

The observed frequencies of events will get closer to the true probabilities as the number of trials increases.

A common, bell-shaped probability distribution where most values cluster around the mean.

The sum of many independent, random variables tends towards a normal distribution.

The idea that the average estimate of a large group can often be more accurate than individual expert judgements.

The reliance on p-values and null hypothesis significance testing in confidence intervals has been criticized for potential misinterpretations and over-reliance on arbitrary significance levels.

Combines prior beliefs with new data using Bayes' theorem to update understanding. It's like learning: start with prior knowledge, get new information, and adjust your beliefs.

The three key components are: Posterior probability (updated belief given observed data), Likelihood (data probability given beliefs), and Prior probability (initial belief estimate).

Main criticisms are subjectivity in choosing prior distributions, computational intensity, historical momentum favoring frequentist methods, and lack of standardization.

Bayesian statistics allows incorporating prior knowledge and updating beliefs based on evidence, while frequentist statistics focuses on long-run frequencies and hypothesis testing.

A subset of individuals from a population used to represent the entire population in a study.

The entire group of individuals that a researcher is interested in studying and drawing conclusions about.

Summary measures used to describe and understand the features of a dataset.

The value representing the center of a distribution, indicating the typical or average value.

The average of all values in a dataset, calculated by summing all values and dividing by the total number of values.

Middle value in a sorted dataset, dividing the data into two halves with equal numbers of values.

The value that appears most frequently in a dataset.

A graphical representation of the distribution of a variable, showing the frequency of each value or range of values.

The difference between the highest and lowest values in a dataset.

The range between the first and third quartiles, representing the middle 50% of the data.

The number of times an event occurs in a series of trials divided by the total number of trials.

Normal distributions represent the complexity of real-world events, where many small factors add up to create a bell-shaped distribution.

A measure of how spread out data points are from the mean. It's calculated by finding the difference of each value from the mean, squaring these differences, summing them up, and then dividing by N-1 (the number of values minus 1).

The sum of the squared differences between each value and the mean. It's a key step in calculating variance.

The process of transforming data to have a mean of 0 and a standard deviation of 1. This allows comparisons across different variables or datasets.

A standardized value that tells you how many standard deviations a single value is away from the mean. Positive Z-scores indicate values above the mean, while negative Z-scores indicate values below the mean.

A measure of the likelihood of a particular event occurring. It can be subjective (based on personal belief), theoretical (based on mathematical reasoning), or experimental (based on observed data).