Statistics & Probability (Oklahoma Academic Standards)

Statistical Questions (S.Q)

• Understand how mathematical and statistical models differ.
  • S.Q.1.1 Tell apart measurement, natural, induced, and sampling variability.
  • S.Q.1.2 Write useful statistical questions to clarify a problem.
• Tell apart populations, sample data, and sampling distributions.
  • S.Q.2.1 Tell sample statistics apart from population parameters.
  • S.Q.2.2 Recognize that a population parameter is fixed but usually unknown.
  • S.Q.2.3 Recognize that sample data are what we observe and come from a population.
  • S.Q.2.4 Recognize a sampling distribution as how a statistic varies over repeated samples.
• Tell categorical and quantitative data apart.
  • S.Q.3.1 Decide whether categorical or quantitative data fits a statistical question.
  • S.Q.3.2 Compare different graphs of the same data set.

Data Collection (S.DC)

• Tell study designs apart and know how far each lets us generalize.
  • S.DC.1.1 Tell apart sample surveys, experiments, and observational studies.
  • S.DC.1.2 Compare the benefits of different sampling methods.
  • S.DC.1.3 Decide how far results can be generalized (scope of inference).
  • S.DC.1.4 Explain how sample size affects how precise a generalization is.
  • S.DC.1.5 Decide when the way data were collected supports a cause-and-effect conclusion.
• Identify sources of bias and the role of randomization.
  • S.DC.2.1 Explain how randomization and bias affect study results.
  • S.DC.2.2 Understand the different roles of random selection and random assignment.

Data Analysis (S.DA)

• Use data distributions to identify key features in context.
  • S.DA.1.1 Summarize shape, center, spread, outliers, and gaps of one-variable data.
  • S.DA.1.2 Choose and make suitable displays for one-variable data.
  • S.DA.1.3 Compare center and spread with statistics that suit the shape of the data.
  • S.DA.1.4 Describe and analyze distributions of one-variable categorical data.
• Fit a normal distribution with mean and standard deviation and estimate percentages.
  • S.DA.2.1 Estimate areas under the normal curve with technology or tables and recognize data sets where it does not fit.
• Compare groups by analyzing their distributions.
  • S.DA.3.1 Make side-by-side displays of distributions.
  • S.DA.3.2 Compare distributions using numerical measures.
• Analyze associations between two variables.
  • S.DA.4.1 Analyze associations with two-way tables and marginal, joint, and conditional frequencies.
  • S.DA.4.2 Predict and draw conclusions from linear, exponential, and quadratic regression models.
  • S.DA.4.3 Analyze scatter plots for patterns, linearity, outliers, and influential points.
  • S.DA.4.4 Find and interpret the correlation coefficient with technology.
  • S.DA.4.5 Understand the risks of extrapolating beyond the data.
• Make statistical inferences and evaluate claims.
  • S.DA.5.1 Build and interpret confidence intervals for a mean and a proportion.
  • S.DA.5.2 Explain how a sample statistic and a confidence level produce a confidence interval.
  • S.DA.5.3 Explain how sample size, confidence level, and standard error change the margin of error.
  • S.DA.5.4 Build intervals for a mean with known standard deviation and for a proportion and use them to test claims.
  • S.DA.5.5 Evaluate claims about a single population parameter with confidence intervals.

Interpreting Results (S.IR)

• Interpret and communicate statistical results in context.
  • S.IR.1.1 Decide whether a difference between two samples is chance variation or significant.
  • S.IR.1.2 Understand confidence level, margin of error, and statistical significance.
  • S.IR.1.3 Draw inferences or predictions that support decisions or recommendations.
  • S.IR.1.4 Write and evaluate recommendations for further research.
• Evaluate what statistical significance, or its absence, means in practice.
  • S.IR.2.1 Build and critique arguments about the practical meaning of significance.
  • S.IR.2.2 Identify lurking variables that might explain an association.
• Evaluate claims and conclusions in the real world.
  • S.IR.3.1 Weigh the strengths and weaknesses of the studies or methods that produced data.
  • S.IR.3.2 Judge whether claims are statistically valid.

Probability (S.P)

• Connect basic probability to statistical analysis.
  • S.P.1.1 Describe events as subsets of a sample space.
  • S.P.1.2 Relate theoretical and experimental probability through the Law of Large Numbers.
  • S.P.1.3 Use counting methods to solve problems and find probabilities of compound events.
• Find joint, conditional, independent, and dependent probabilities and interpret them.
  • S.P.2.1 Test for independence by checking whether the joint probability equals the product of the probabilities.
  • S.P.2.2 Find the conditional probability of A given B.
  • S.P.2.3 Interpret independence as the conditional probability equaling the unconditional one.
• Use probability to make decisions.
  • S.P.3.1 Analyze decisions and strategies with probability and expected value.
  • S.P.3.2 Analyze decisions about significance based on reported p-values.