Download Skills We`ve Learned This Semester Think: Be able to identify the

Skills We’ve Learned This Semester
1. Think: Be able to identify the Who, What, When, Where, Why, and hoW of data, or recognize when some of this
information has not been provided.
2. Think: Be able to identify the cases and variables in any data set.
3. Think: Be able to classify a variable as categorical or quantitative depending on its use.
4. Think: For any quantitative variable be able to identify the units in which the variable has been measured (or
note that they have not been provided).
5. Tell and be able to describe a variable in terms of its Who, What, When, Where, Why, and hoW (and be
prepared to remark when that information is not provided.)
6. Think and be able to recognize when a variable is categorical and choose an appropriate display for it.
7. Think and understand how to examine the association between categorical variables by comparing conditional
and marginal percentages.
8. Show and be able to summarize the distribution of a categorical variable with a frequency table.
9. Show and be able to display the distribution of a categorical variable with a bar chart or pie chart.
10. Show and know how to make and examine a contingency table.
11. Show and know how to make and examine displays of the conditional distributions of one variable for 2 or more
groups.
12. Tell and be able to describe the distribution of a categorical variable in terms of its possible values and relative
frequencies.
13. Tell and know how to describe any anomalies or extraordinary features revealed by the display of a variable.
14. Tell and be able to describe and discuss patterns found in a contingency table and associated displays of
conditional distributions.
15. Think and Be able to identify an appropriate display for any quantitative variable.
16. Think and be able to guess the shape of the distribution of a variable by knowing something about the data.
17. Show and know how to display the distribution of a quantitative variable with a stem and leaf display (by hand
for smaller data sets), a dot plot, or a histogram (made by calculator for large data sets).
18. Show and know how to make a time plot of data that may vary over time.
19. Tell and be able to describe the distribution of a quantitative variable by CUSS and BS (Centers, Unusual, Shapes,
Spread).
20. Tell and be able to describe any anomalies or extraordinary features revealed by the display of a variable.
21. Tell and know how to compare the distribution of 2 or more groups by comparing their shapes, enters, and
spreads.
22. Tell and know how to describe patterns over time show in a time plot.
23. Tell and be able to discuss any outliers in the data, noting how they deviate from the overall pattern of the data.
24. Think and be able to select a suitable measure of center and a suitable measure of spread for a variable based
on information about its distribution.
25. Think and know the basic properties of the median: The median divides the data into the half of the data values
that are below the median and the half that are above the median.
26. Think and know the basic properties of the mean: The mean is the point at which the histogram balances and
gives an average of the data.
27. Think and know that the standard deviation summarizes how spread out all the data are around the mean.
28. Show and know how to compute the mean and median of a set of data.
29. Shoe and know how to compute the standard deviation and IQR of a set of data.
30. Show and be able to create a 5-number summary of a variable.
31. Show and understand that the median and IQR resist the effects of outliers, while the mean and standard
deviation do not.
32. Show and understand that in a skewed distribution, the mean is pulled in the direction of skewness (toward the
longer tail) relative to the median.
33. Tell and know how to describe summary measures in a sentence. In particular, know that the common measure
of center an spread have the same units as the variable that they summarize, and should be described in those
units.
34. Tell and be able to describe the distribution of a quantitative variable with a description of the shape of the
distribution, a numerical measure of center, and numerical measure of spread in context. Be sure to note any
unusual features, such as outliers, and gaps too.
35. Tell and know how to compare the distributions of 2 or more groups by comparing their shapes, centers and
spreads.
36. Tell and be able to compare 2 or more groups by comparing their boxplots.
37. Tell and know how to use the 1.5 IQR rule to identify possible outliers. Interpret outliers found in boxplots made
on a calculator.
38. Think and understand how adding and subtracting a constant or multiplying or dividing by a constant changes
the center and/or spread of a variable.
39. Think and recognize when standardization can be used to compare values..
40. Think and understand that standardizing uses the standard deviation as a ruler.
41. Think and recognize when a Normal model is appropriate.
42. Show and know how to calculate the z-score of an observation.
43. Show and be able to use Normal models and the 68-95-99.7 Rule to estimate the percentage of observations
falling within 1, 2, or 3 standard deviations of the mean.
44. Show and know how to find the percentage of observations falling below any value in a Normal model using a
Normal table or appropriate technology.
45. Show and know how to check whether a variable satisfies the nearly Normal Condition by making a Normal
probability plot or a histogram.
46. Tell and know what z-scores mean.
47. Tell and be able to explain how extraordinary a standardized value may be by using a Normal model.
48. Think and recognize when interest in the pattern of possible relationship between 2 quantitative variables
suggest making a scatterplot.
49. Think and know how to identify the roles of the variables and to place the response variable on the y axis and
the explanatory variable on the x axis.
50. Think and know the conditions for correlation and how to check them.
51. Think and know that correlations are between -1 and +1, and that each extreme indicates a perfect linear
association in the positive or negative direction of the correlation.
52. Think and understand how the magnitude of the correlation reflects the strength of a linear association as
viewed in a scatterplot.
53. Think and know that the correlation has no units.
54. Think and know that the correlation coefficient is not changed by changing the center of scale of either variable.
55. Think and understand that causation cannot be demonstrated by a scatterplot or correlation.
56. Show and know how to make a scatterplot by hand (for a small set of data) or with technology.)
57. Show or know how to compute the correlation of 2 variables.
58. Show and know how to read a correlation table produced by a statistics program on the calculator.
59. Tell and be able to describe the direction form, and strength of a scatterplot.
60. Tell and be prepared to identify and describe points that deviate from the overall pattern.
61. Tell and be able to use correlation as part of the description of a scatterplot.
62. Tell and be alert to misinterpretations of correlation.
63. Tell and Understand that finding a correlation between 2 variables does not indicate a causal relationship
between them. Beware the dangers of suggesting causal relationships when describing correlations.
64. Think and be able to identify response (y) and explanatory (x) variables in context.
65. Think and understand how a linear equation summarizes the relationship between 2 variables.
66. Think and recognize when a regression should be used to summarize a linear relationship between 2
quantitative variables.
67. Think and be able to judge whether the slope of a regression makes sense.
68. Think and know how to examine your data for violations of the Straight Enough Condition that would make it in
appropriate to compute a regression.
69. Think and understand that the least squares slope is easily affected by extreme values.
70. Think and know that residuals are the differences between the data values and the corresponding values
predicted by the line and that the least squares criterion finds the line that minimizes the sum of the squared
residuals.
71. Think and know how to use a plot of residuals against predicted values to check the Straight Enough condition or
look for outliers.
72. Show and know how to find a regression equation from the summary statistics for each variable and the
correlation between the variables.
73. Show and know how to find a regression equation using your statistics software and how to find the slope and
intercept values in the regression output table.
74. Show and know how to use regression to predict a value of y for a given x.
75. Show and know how to compute the residual for each data value and how to display them.
76. Tell and be able to write a sentence explaining what a linear equation says about the relationship between y and
x, basing it on the fact that the slope is given in y-units per x – units.
77. Tell and understand how the correlation coefficient and the regression slope are related. Know how 𝑅 2
describes how much of the variation in y is accounted for by its linear relationship with x.
78. Tell and be able to describe a prediction made from a regression equation, relating the predicted value to the
specified x-value.
79. Think and understand that we cannot fit linear models or use linear regression if the underlying relationship
between the variables is not itself linear.
80. Think and understand that data used to find a model must be homogeneous. Look for subgroups in data before
you find a regression, and analyze each separately.
81. Think and know the danger of extrapolating beyond the range of the x-values used to find the linear model,
especially when the extrapolation tries to predict into the future.
82. Think and understand that points can be unusual by having a large residual or by having high leverage.
83. Think and understand that an influential point can change the slope and intercept of the regression line.
84. Think and look for lurking variables whenever considering the association between 2 variables. Understand that
a strong association does not mean that the variables are causally related.
85. Think and know how to display residuals from a linear model by making a scatterplot of residuals against
predicted values or against the x variable, and know what patterns to look for in the picture.
86. Show and Know how to display residuals from a linear model by making a scatterplot of the data and how to
look for points with large residuals by examining a scatterplot of the residuals against predicted values or
against the x variable. Understand how fitting a regression line with and without influential points can add to
understanding of the regression model.
87. Show and know how to look for high leverage points by examining the distribution of the x values or by
recognizing them in a scatterplot of the data, and understand how they can affect a linear model.
88. Tell and include diagnostic information such as plots of residuals and leverages as part of your report of a
regression.
89. Tell and report any high leverage points.
90. Tell and report any outliers. Consider reporting analyses with and without outliers included to assess their
influence on the regression.
91. Tell and include appropriate cautions about extrapolation when reporting predictions from a linear model.
92. Tell and discuss possible lurking variables.
93. Think and recognize when a well-chosen re-expression may help you improve and simplify your analysis
94. Think and understand the value of re-expressing data to improve symmetry, to make the scatter around a line
more constant, or to make a scatterplot more linear.
95. Think and recognize when the pattern of the data indicates that no re-expression can improve the structure of
the data.
96. Show and know how to re-express data with powers and how to find an effective re-expression for your dta
using your statistics calculator.
97. Show and be able to reverse any of the common re-expressions to put a predicted value or residual back into
the original units from a re-expression.
98. Tell and be able to describe a summary or display of a re-expressed variable making clear how it was reexpressed and giving its re-expressed units.
99. Tell and be able to describe a regression model fit to re-expressed data in terms of the re-expressed variables.