STATS 101/108 - Module 1

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Chapters 1-4

Statistics

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85 Terms

1
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What are the three main reasons for generating and analysing data?

Description, prediction, explanation.

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Description

Describing the features of a dataset or population of interest, This involves calculating estimates based on groups and identifying clusters.

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Prediction

Predict what will happen in a new instance or a future time. This involves making forecasts at the individual level.

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Explanation

Explain why things have happened, often so that we can change how the happen in the future. This involves discovering and investigating cases.

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Entity/case

Each entry in a dataset.

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Variable/attribute

Features or properties of an entity.

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What are the two kinds of variable?

Numerical and categorical.

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Numerical variable

Variables describing a measurable characteristic.

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Categorical variable

Variables describing the different groups an entity belongs to.

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Rectangular data set

A form of storing data where each row corresponds to an entity and each column corresponds to a variable.

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Classification

Identifying and grouping entities into predetermined levels.

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Cross-classification

Creating groups based on combinations of levels from two categorical variables

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Two-way table of counts

A type of summary table that allows us to calculate the proportions in the data.

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Classification model

A model that predicts the level/group for a target categorical variable.

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Training data

The data used to create a prediction model.

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Binary classification model

A classification model that predicts which of two groups an entity is in.

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Proportion

The fraction of the total that possesses a certain attribute.

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How can proportions be expressed?

As a fraction, decimal, or percentage.

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Baseline model

A no-information model that always predicts the level with the highest proportion in the training data.

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Confusion matrix

A type of two-way table where the two categorical variables relate to the success of the classification model.

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What are the two categorical variables in a confusion matrix?

Actual value and predicted value.

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Percentage correctly classified (PCC)

The proportion of predictions where the actual and predicted values match.

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How is the PCC caluclated?

By adding the values in the main diagonal and dividing by the total.

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Conditional proportions

Used to calculate the PCC for different levels of the data.

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Why are conditional proportions used?

To find out if a model is better or worse at identifying a particular variable.

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What common displays are used for numeric data?

Dot plot and box plot.

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How are numeric displays ordered?

Low-to-high along the x-axis.

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Dot plot

Display that shows each value as a dot and stacks similar values on top of each other.

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Box plot

Display that only shows the minimum, lower quartile, median, upper quartile, and maximum of the values.

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What are the two measures of centre?

Median and mean.

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Median

The middle value of the distribution.

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Mean

The average value of the distribution.

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Distribution

Different shapes made by the dot plot.

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Positively skewed

Most data is low, but some extreme values create a long tail and pull the mean up.

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Negatively skewed

Most data is high, but some extreme values create a long tail and pull the mean down.

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In a positively skewed distribution, the mean is ____ than the median.

higher

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In a negatively skewed distribution, the mean is ____ than the median.

lower

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Symmetric

The data is evenly distributed.

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Unimodal

There is one peak in the distribution.

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Bimodal

There are two peaks in the distribution.

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Variation

How close the values are together.

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Interquartile range (IQR)

The difference between the upper and lower quartiles. The middle 50% of the distribution is here.

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Standard deviation

How close, on average, values are to the mean.

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A larger standard deviation indicates that the values are ____ from the mean on average, so there is ____ variation.

further away, more

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A smaller standard deviation indicates that the values are ____ to the mean on average, so there is ____ variation.

closer, less

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Testing data

Data used to test a classification model.

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Algorithm

A set of instructions for using input data to predict which level a group belongs to.

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Decision rule

A type of algorithm used in classification models.

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Algorithmic bias

The ways that the data and assumptions in the development of an algorithm can result in unfair or inaccurate outcomes.

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Dynamic data

Data that is updated periodically as new data becomes available.

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Target/response variable

The variable we are trying to predict.

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Prediction error

The difference between the actual value and the predicted value.

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Positive prediction error occurs when the actual value is ____ than the predicted value.

higher

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Negative prediction error occurs when the actual value is ____ than the predicted value.

lower

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No-information model for a numerical variable

Always predicts the mean.

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Prediction interval

Gives a range of values for the prediction, between an upper and lower limit.

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How much of the training data is the prediction interval based on?

The middle 95% of the data.

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What two features need to be balanced in a prediction interval?

Accuracy and precision.

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Accuracy

How often a model gets the prediction correct

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Precision

How close the predictions are to the actual values.

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Scatter plot

A plot with two numerical variables used to visualise the association between the variables.

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What features should be checked on a scatter plot?

Association, pattern/trend, scatter/variation.

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Explanatory variable

The indepedent variable.

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What axis is the explanatory variable plotted on?

The x-axis.

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What axis is the response variable plotted on?

The y-axis.

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Response variable

The dependent variable - what we are trying to predict.

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Correlation

A measure of association strength between two variables.

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Rank correlation

Measure of how well the variables match up if ordered from smallest to largest.

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Linear model

A straight line that goes through the centre of the data - a line of best fit - that is used to make a point prediction.

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Residual

The prediction error used in a linear model.

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What is used as the residual in a linear model?

A prediction error that contains 95% of the data.

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Why is the middle 95% of the distribution used?

It shows us where the likely/usual values for the distribution are.

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Tail proportion

The proportion of values that are above or below a value of interest.

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If the tail proportion is less than 2.5%, it can be considered ____ for the distribution.

unusual

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If the tail proportion is more than 2.5%, it can be considered ____ for the distribution.

usual

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Null model

A baseline model used to account for any uncertainty in the process that may have led to the observed result.

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Null hypothesis

The “just chance” explanation for a particular situation.

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Chance variation

Explanation for why even if the underlying proportion is a certain value, we may not see this proportion when generating data from the model.

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Experiment

A study in which the researcher will control, manipulate, or change the conditions the experimental units experience.

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Random variation

Differences in group summaries and nothing else, e.g. due to random allocation to groups.

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Reference distribution

A distribution showing the random variation.

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Random allocation

Experimental unit are allocated to treatments such that it is equally likely that each treatment is applied to each unit/

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Randomisation test

A test producing a reference distribution of what could be explained by ‘just chance’.

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If the tail proportion of the observed result is less than 2.5% in the reference distribution, it is ____ with the null model and ____ a result of chance.

not compatible, not likely

85
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If the tail proportion of the observed result is more than 2.5% in the reference distribution, it is ____ with the null model and ____ a result of chance.

compatible, could be