Probability and Theoretical Distributions

To infer characteristics about a larger population.

A meaningful, non-random pattern observed in the sample data.

Variability in the data due to randomness.

<p>It represents the probability of event B occurring, given that event A is true.</p> Signup and view all the answers

<p>Event A represents whether or not it is rush hour.</p> Signup and view all the answers

<p>Because each member of the population has an equal chance of being included.</p> Signup and view all the answers

<p>The probability is 1 or 100%.</p> Signup and view all the answers

<p>Noise, which is variability due to random chance.</p> Signup and view all the answers

<p>That one coin flip outcome does not influence any other flip.</p> Signup and view all the answers

<p>It allows us to assess the probability of observing our data given a certain assumption about the absence of an effect or relationship.</p> Signup and view all the answers

<p>A higher proportion of vaping at work reported by the men in the study.</p> Signup and view all the answers

<p>They must try to find meaningful, probable signals.</p> Signup and view all the answers

<p>We assume that no signal exists.</p> Signup and view all the answers

<p>It is assumed that men and women vape the same amount at work.</p> Signup and view all the answers

<p>This is done to assess the probability of observing the data, given our assumption that no signal exists.</p> Signup and view all the answers

<p>Experience represents the sample data used to decide the best route, based on past commutes under similar conditions.</p> Signup and view all the answers

<p>Statistics can feel intimidating because it is often presented as complex mathematical equations, distributions, and using Greek letters and tables.</p> Signup and view all the answers

<p>The core purpose is to assess the probability of observed data given some assumption.</p> Signup and view all the answers

<p>The notation is $P(x)$.</p> Signup and view all the answers

<p>It represents the probability that the next coin flip will result in heads.</p> Signup and view all the answers

<p>The probability of either outcome is 1 or 100% and this is written as $P(A = heads OR A = tails)$.</p> Signup and view all the answers

<p>Formalizing probability allows us to understand and test probabilistic decision-making.</p> Signup and view all the answers

<p>No, Google Maps cannot predict a car crash before it happens.</p> Signup and view all the answers

<p>To use data from a sample to infer information about a larger population.</p> Signup and view all the answers

<p>The number of individuals within a sample.</p> Signup and view all the answers

<p>Because it's often impractical or impossible to survey entire populations due to their large size.</p> Signup and view all the answers

<p>Any effect or difference that is observed in a sample.</p> Signup and view all the answers

<p>To understand and assess probability.</p> Signup and view all the answers

<p>They provide a probabilistic measure of how likely it is that the signal observed in the sample reflects the broader population.</p> Signup and view all the answers

<p>A population is a broader group of interest, while a sample is a subset of that population used for data collection.</p> Signup and view all the answers

<p>To get comfortable with inferential statistics techniques.</p> Signup and view all the answers

<p>A larger numerator, representing the 'signal', suggests a stronger signal is present in the sample data.</p> Signup and view all the answers

<p>A larger denominator, representing the 'noise', decreases the overall ratio.</p> Signup and view all the answers

<p>A stronger signal in a sample makes it more probable that a signal exists at the population level.</p> Signup and view all the answers

<p>Noise refers to random variations or obscuring factors that weaken or hide the actual signal.</p> Signup and view all the answers

<p>To determine probability, by examining how probable that the signal observed is representative of the broader population.</p> Signup and view all the answers

<p>Falsification involves determining if something is improbable, leading to an assumption that an alternate reality is true. It is used because we cannot know what is true for a population.</p> Signup and view all the answers

<p>The initial assumption is that no signal exists at the population level.</p> Signup and view all the answers

<p>Confirmation by contradiction means assuming there is no signal, and then assessing if the sample data is improbable under that assumption.</p> Signup and view all the answers

<p>The initial assumption is that the signal does not exist in the overall population.</p> Signup and view all the answers

<p>No, it doesn't seem significant. A 2% difference could easily occur due to random chance or noise in the sample.</p> Signup and view all the answers

<p>A large difference suggests that the initial assumption of no signal may be wrong and should be rejected.</p> Signup and view all the answers

<ol> <li>assume no signal exists, 2) measure signal and noise in the sample, 3) assess probability of the data if no signal exists.</li> </ol> Signup and view all the answers

<p>The initial assumption is that there is a 50% chance of flipping heads on any flip.</p> Signup and view all the answers

<p>Yes, this would be a good reason to question the 50% chance. Getting 72 heads out of 100 seems unlikely under the assumption of a fair coin.</p> Signup and view all the answers

<p>Noise refers to random variability in the sample, such as interviewing a few men who happen to vape more at work than most men.</p> Signup and view all the answers

<p>The overall goal is to make educated guesses based on the data that is available.</p> Signup and view all the answers

The measure of the likelihood that an event will occur.

Mathematical models that describe the expected frequency of outcomes in a probability experiment.

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

Techniques that allow conclusions about a population based on a sample.

The complete set of items or people you want to learn about in a study.

A subset of the population selected for a study.

The observed effect or difference in a dataset that suggests a trend or result.

A symbol representing the number of individuals in a sample.

Random variability in data that obscures meaningful signals.

A sample in which each individual of a population has an equal chance of being selected.

An example illustrating randomness, where outcomes are independent with expected probabilities.

The natural differences observed in sample data due to random selection.

The distinction between meaningful data patterns and random variability.

Mathematical notation to express probability of an event, e.g., P(x).

The probability that the next coin flip results in heads.

Using past experiences or data to inform current decisions.

Combining probabilities of multiple outcomes, e.g., heads or tails.

Grasping probability concepts without complex math.

Formal approaches to assess and interpret data probability.

Choosing actions based on the probability of various outcomes.

The probability of an event occurring given another event is true.

This notation means the probability of B occurring, given that A is true.

Conditional probability can be explored even if A is not true; it's theoretical.

An example where A represents rush hour affecting the probability of B (the freeway being fastest).

This probability equals 1, indicating the freeway is always fastest when not during rush hour.

This probability equals 1/3, suggesting the freeway is fastest only 33.3% of the time during rush hour.

Evaluating the probability of observed data assuming no relationship exists (e.g., smoking and cancer).

The initial assumption that no difference exists in the population.

Making choices based on the likelihood of outcomes based on available data.

The process of disproving an initial assumption based on evidence.

Assessing how often specific outcomes occur to understand the data.

Using coin flips to demonstrate the principles of probability in statistics.

Making informed decisions based on statistical analysis of data.

The ratio comparing a desired signal to background noise.

The process of proving something is improbable or false.

Methods to analyze data, finding signals amidst noise.

The assumption that no signal exists at the population level.

Data collected from a subset of a broader population.

An observation that is considered likely based on data analysis.