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Essential Statistics

This guide covers the fundamental concepts and techniques of statistics, including definitions, relationships, data analysis, sampling, permutations, combinations, qualitative and quantitative data, measures of center, distribution shapes, measures of variation, measures of position, correlation, and regression analysis.

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Essential Statistics

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  1. Essential Statistics (a.k.a: The statistical bare minimum I should take along from STAT 101)

  2. Essentials: The Nature of Statistics(a.k.a: The bare minimum I should take along from this topic.) • Definitions and relationships as presented on the sheet Anatomy of the Basics: Statistical Terms and Relationships • Identification of variables and their characteristics • Careful review of data and their presentation • Providing a context for the data • Why percentages and not numeric counts when making comparisons

  3. Essentials: Sampling(stuff I should know) • General types of data collection • Importance of randomization in obtaining samples • Sampling Error • Difference between non-probability sampling and probability sampling • Different types of random samples and how each is obtained • Ability to obtain samples using probability sampling approaches

  4. Essentials:Permutations & Combinations(So that’s how we determine the number of possible samples!) • Definitions: Permutation; Factorial; Combination. • What a Factorial is and how to use it. • Ability to determine the number of permutations or combinations resulting from a stated situation. • Extras here: Tree diagrams & the multiplication rule.

  5. Essentials:Qualitative Data(Be able to address the following.) • Characteristics of qualitative variables. • Building a qualitative frequency table. • Appropriate charts/graphs for qualitative data (and how to make them).

  6. Essentials:Quantitative Data(Know this stuff - a useful filler term in stats.) • Characteristics of quantitative variables. • Building a quantitative frequency table. • From within a quantitative frequency table, be able to identify: classes, class widths, class midpoints, class limits, boundaries (cutpoints) • Identify and construct appropriate charts/graphs for quantitative data.

  7. Essentials:Sigma - S(Yeah, I got this – so everyone thinks, but it isn’t as easy as it looks.) • Understand what Sigma (S) means and how it is used. • Be able to interpret what S is telling you to do in a given formula. • When you think you’ve got it, practice some more.

  8. Essentials: Measures of Center(The great mean vs. median conundrum.) • Be able to identify the characteristics of the median, mean and mode, and to which types of data each applies. • Be able to calculate the median, mean and mode, as appropriate, for a set of data. • Affected by vs. resistant to extreme values. What are the implications for the mean and median?.

  9. Essentials:Distribution Shapes(Lots of them , but we will focus on three main types.) • Be able to explain what constitutes a distribution. • Be able to identify Left, Right and Normal distributions (and a Uniform distribution). • Be able to determine if a distribution is normally distributed or skewed through use of a formula or computer software and, be able to interpret the results of this process.

  10. Essentials:Measures of Variation(Variation – a must for statistical analysis.) • Know the types of measures used to look at variation and the type data to which they apply. • Be able to calculate the range, standard deviation and inter-quartile range. • Be able to determine the distance away from the mean a given value lies in terms of standard deviations (think z-score). • Be able to apply the Empirical Rule and Chebychev’s Theorem to specific situations.

  11. Essentials:Measures of Position(Better understanding distribution shapes.) • Know the types of measures used to look at specific positions within a data distribution. • Be able to calculate the inter-quartile range, three quartiles, Pearson’s Index of Skewness, z-score, Coefficient of Variation. • Be familiar with symmetry vs. skewness and distribution shapes. • Be able to build both traditional and modified box plots (aka: box-and-whiskers plot).

  12. Essentials: Correlation(The invalid assumption that correlation implies cause is probably among the two or three most serious and common errors of human reasoning. --Stephen Jay Gould, The Mismeasure of Man.) • Correlation – potential relationships, not causality. • Know the steps one might employ before obtaining a correlation. • Know the characteristics of the Pearson Product Moment Correlation Coefficient (for us the correlation). • Be able to calculate a correlation and determine if it is statistically significant. • Be able to create a scatter plot of the paired data being studied. • Be able to determine the directionality of a correlation and its strength via formula and observation of plotted data.

  13. Essentials:Regression(Predictions based upon the known.) • Understand what the regression process does - prediction. • Be able to state the steps we use leading up to the decision to conduct regression. • Be able to calculate the slope of a line and the y-intercept. • Be able to calculate a regression equation and apply it to the prediction of other values. Know that these are estimates, not necessarily the actual values that might occur. • Know what the Least Squares Property and Line of Best Fit. Residual – what’s that?

  14. Essentials:Normal Distribution(I’m normal...or am I?) • Be able to identify normal and approximately normal distributions. • Know the characteristics of the Standard Normal. • Be able to use the Standard Normal table. • Empirical Rule and the Standard Normal. • Transforming Non-Standard distributions to the Standard Normal.

  15. Essentials:Distribution of Sample Means(A distribution unlike others) • Be able to explain what the Distribution of Sample Means represents. • Know the three characteristics of this distribution. • Be able to use a set of data demonstrate the calculation of the mean and standard deviation of this distribution. • What is a statistically large sample?

  16. Essentials:Confidence Intervals(How sure we are.) • Inferential statistics, precision and the margin of error. • Obtaining a confidence interval. • Za/2 • Guinness, Gosset & the Student’s t Distribution • Confidence Intervals for large and small samples, and proportions.

  17. Essentials:Hypothesis Testing(Testing Claims.) • What is a hypothesis. • Null vs. Alternative hypotheses • Statistical Significance: • Critical Values & p-values • One-sample Tests for mean & proportions

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