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Statistics
Introduction to Statistics

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation,
presentation, and organization of data
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This study note aims to provide an
overview of the key concepts and techniques used in statistics
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Qualitative data is nonnumerical in nature and describes characteristics or attributes of a population or sample
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Quantitative data, on the other hand, is numerical and can be measured or counted
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Discrete data can only take on whole
numbers, such as the number of children in a family, whereas continuous data can take on any value
within a range, such as height or weight
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It includes measures of central tendency, such as mean, median, and mode, which are
used to summarize the data in a single value
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The median is the middle value in the dataset, and the
mode is the value that occurs most frequently
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Examples of measures of dispersion include the range, variance, and standard
deviation
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Inferential Statistics

Inferential statistics is the branch of statistics that deals with making inferences about a population
based on a sample
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One of the key techniques used in inferential statistics is hypothesis
testing, which involves setting up a null hypothesis (the hypothesis of no effect) and an alternative
hypothesis (the hypothesis of an effect) and using statistical tests to determine whether the null
hypothesis can be rejected in favor of the alternative hypothesis
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Confidence intervals are based on the sample data and the standard error of the mean
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It is a key concept
in statistics and is used to describe the likelihood of an event occurring
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The probability of an event can be calculated using the following formula:

P(event) = number of favorable outcomes / total number of outcomes

In addition to the basic probability rules, such as the addition rule and the multiplication rule, other
important concepts in probability include conditional probability, which is the probability of an event
given that another event has occurred, and the law of large numbers, which states that as the sample
size increases, the sample mean approaches the population mean
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The
purpose of sampling is to obtain information about the population while minimizing the cost and time
involved in collecting data from the entire population
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Probability
sampling involves selecting individuals from the population at random, ensuring that each individual has
an equal chance of being selected
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Non-probability sampling, on the other hand, involves selecting individuals from the
population based on non-random criteria, such as convenience or judgement
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To minimize sampling error, it is important to have a large sample
size and to use appropriate sampling techniques
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The dependent variable is the variable being predicted
or explained, while the independent variable is the variable that is used to make the prediction
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Simple linear regression involves a single independent variable, while multiple linear regression involves
two or more independent variables
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The quality of the model can be
assessed using the coefficient of determination, also known as R-squared, which measures the
proportion of the variance in the dependent variable that is explained by the independent variables
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It involves identifying the research question, selecting the sample, and controlling for potential
sources of bias
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Between-subjects design involves assigning participants to different groups and comparing the results
between the groups
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Other important aspects of experimental design include randomization, which involves randomly
assigning participants to different groups or conditions, and blinding, which involves withholding
information from the participants or the experimenters to reduce bias
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Key concepts
and techniques include data types, descriptive statistics, inferential statistics, probability, sampling,
regression analysis, and experimental design
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