"The discipline that concerns the collection, organization, analysis, interpretation, and presentation of data."
A basic overview of what statistics is, its relevance in various fields, and the different types of statistical analysis.
Descriptive Statistics: Involves the collection, organization, and summarization of data, through measures of central tendency such as mean, median, and mode, and measures of variability such as range, variance, and standard deviation.
Inferential Statistics: Involves making generalizations about a population based on a sample of data, and includes hypothesis testing and estimation.
Probability: The likelihood of an event occurring, usually measured as a number between 0 and 1.
Random Variables: Variables that take on different values with different probabilities, often used in probability distributions.
Probability Distributions: Mathematical functions that describe the likelihood of different outcomes in a random event, such as a coin toss or dice roll.
Normal Distribution: A common probability distribution that is symmetric and bell-shaped, with a mean and standard deviation that determine its exact shape.
Central Limit Theorem: A statistical principle that states that the means of random samples taken from a population will tend to be normally distributed, regardless of the shape of the population distribution.
Sampling Techniques: Methods for selecting a representative subset of a population to be studied, including simple random sampling, stratified sampling, and cluster sampling.
Confidence Intervals: A range of values that is likely to contain the true population parameter, with a specified level of confidence.
Hypothesis Testing: A method of determining whether a hypothesis about a population parameter is supported by the sample data, using statistical significance tests such as p-values and the t-test.
Correlation: A measure of the strength and direction of the relationship between two variables, such as age and income or height and weight.
Regression: A statistical method for predicting the value of one variable (the dependent variable) based on the values of one or more other variables (the independent variables).
ANOVA: Analysis of variance, used to compare means among more than two groups.
Chi-Square Test: A statistical test used to determine whether there is a significant difference between the expected and observed frequencies in a contingency table.
Nonparametric Statistics: Statistical methods that do not rely on any assumptions about the underlying probability distribution, and can be useful when data is not normally distributed.
Descriptive Statistics: This type of statistics deals with summarizing, describing and analyzing data by using measures like mean, median, mode, variance, and standard deviation.
Inferential Statistics: This type of statistics uses statistical models and sample data to make inferences about populations.
Probability: This type of statistics deals with calculating the likelihood of an event occurring under certain conditions or circumstances based on mathematical principles.
Biostatistics: This type of statistics uses various statistical models and methods to study and analyze data related to biological and medical research.
Econometrics: This type of statistics combines statistical methods, economic theory and mathematical modelling to analyze economic data and predict economic trends.
Spatial Statistics: This type of statistics deals with analyzing and modeling data that is distributed over space, such as maps and geographic data.
Time Series Analysis: This type of statistics involves analyzing patterns and trends in time-series data, such as sales data, weather data, or stock price data.
Bayesian Statistics: This type of statistics involves using probability to assign probabilities to different hypotheses and predictions about data.
Social Statistics: This type of statistics deals with the analysis of data related to social phenomena such as demographics, education, and crime.
Multivariate Statistics: This type of statistics deals with analyzing data with multiple variables, such as analyzing the relationship between income and education level.
"Collection, organization, analysis, interpretation, and presentation of data."
"Populations can be diverse groups of people or objects such as 'all people living in a country' or 'every atom composing a crystal'."
"Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole."
"Statisticians collect data by developing specific experiment designs and survey samples."
"An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation."
"Descriptive statistics" and "inferential statistics."
"Descriptive statistics summarize data from a sample using indexes such as the mean or standard deviation."
"Inferential statistics draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation)."
"Central tendency (or location)" and "dispersion (or variability)."
"The framework of probability theory, which deals with the analysis of random phenomena."
"A hypothesis is proposed for the statistical relationship between two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets."
"Type I errors (null hypothesis is falsely rejected giving a 'false positive')" and "Type II errors (null hypothesis fails to be rejected and an actual relationship between populations is missed giving a 'false negative')."
"Random (noise) or systematic (bias) errors" and "other types of errors (e.g., blunder, such as when an analyst reports incorrect units)."
"The presence of missing data or censoring may result in biased estimates."
"Obtaining a sufficient sample size" and "specifying an adequate null hypothesis."
"Inferential statistics are made under the framework of probability theory."
"When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples."
"Descriptive statistics are most often concerned with two sets of properties of a distribution: central tendency (or location) and dispersion (or variability)."
"Inferential statistics draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation)."