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Essential Statistics

Essential Statistics. ( a.k.a : The statistical bare minimum I should take along from STAT 101). Essentials: The Nature of Statistics ( a.k.a : The bare minimum I should take along from this topic.).

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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?

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