Statistical Reasoning

MASR: Statistical Reasoning

MASR.A: Statistics

MASR.A.1: apply the statistical method to real-world situations

MASR.A.2: formulate questions to clarify the problem at hand and formulate one (or more) questions that can be answered with data

MASR.A.3: collect data by designing a plan to collect appropriate data and employ the plan to collect the data

MASR.A.4: analyze data by selecting appropriate graphical and numerical methods and using these methods to analyze the data

MASR.A.5: interpret results by interpreting the analysis and relating the interpretation to the original question

MASR.A.6: identify whether the data are categorical or quantitative (numerical)

MASR.A.7: identify the difference between categorical and quantitative (numerical) data

MASR.A.8: determine the appropriate graphical display for each type of data

MASR.A.9: determine the type of data used to produce a given graphical display

MASR.A.10: distinguish between a population distribution, a sample data distribution, and a sampling distribution

MASR.A.11: identify the three types of distributions

MASR.A.12: recognize a population distribution has fixed values of its parameters that are usually unknown

MASR.A.13: recognize a sample data distribution is taken from a population distribution and the data distribution is what is seen in practice hoping it approximates the population distribution

MASR.A.14: recognize a sampling distribution is the distribution of a sample statistic (such as a sample mean or a sample proportion) obtained from repeated samples; the sampling distribution provides the key for determining how close to expect a sample statistic approximates the population parameter

MASR.A.15: create sample data distributions and a sampling distribution

MASR.A.16: create a sample data distribution by taking a sample from a defined population and summarizing the data in a distribution

MASR.A.17: create a sampling distribution of a statistic by taking repeated samples from a population (either hands-on or by simulation with technology)

MASR.A.18: understand that randomness should be incorporated into a sampling or experimental procedure

MASR.A.19: implement a reasonable random method for selecting a sample or for assigning treatments in an experiment

MASR.A.20: implement a simple random sample

MASR.A.21: randomly assign treatments to experimental subjects or objects

MASR.A.22: distinguish between the three types of study designs for collecting data (i.e., sample survey, experiment, and observational study) and will know the scope of the interpretation for each design type

MASR.A.23: determine the type of study design appropriate for answering a statistical question

MASR.A.24: determine the appropriate scope of inference for the study design used

MASR.A.25: distinguish between the role of randomness and the role of sample size with respect to using a statistic from a sample to estimate a population parameter

MASR.A.26: distinguish the roles of randomization and sample size with designing studies

MASR.A.27: recognize that randomization reduces bias where bias occurs when certain outcomes are systematically more likely to appear

MASR.A.28: recognize that random selection from a population plays a different role than random assignment in an experiment

MASR.A.29: recognize that sample size impacts the precision with which estimates of the population parameters can be made (i.e., larger the sample size the more precision)

MASR.A.30: use distributions to identify the key features of the data collected

MASR.A.31: describe the distribution for quantitative and categorical data

MASR.A.32: describe and interpret the shape of the distribution

MASR.A.33: describe and interpret the measures of center for the distribution

MASR.A.34: describe and interpret the patterns in variability for the distribution

MASR.A.35: describe and interpret any outliers or gaps in the distribution

MASR.A.36: describe and interpret the modal category for the distribution

MASR.A.37: describe and interpret patterns that exist for the distribution

MASR.A.38: use distributions to compare two or more groups

MASR.A.39: compare two or more groups by analyzing distributions

MASR.A.40: construct appropriate graphical displays of distributions

MASR.A.41: use graphical and numerical attributes of distributions to make comparisons between distributions

MASR.A.42: determine if an association exists between two variables (e.g., pattern or trend in bivariate data) and use values of one variable to predict values of another variable

MASR.A.43: analyze associations between variables and make predictions from one variable to another

MASR.A.44: analyze associations between two variables

MASR.A.45: create scatter plots for two-variable numerical data

MASR.A.46: create two-way tables for two-variable categorical data

MASR.A.47: analyze patterns and trends in data displays

MASR.A.48: make predictions and draw conclusions from two-variable data based on data displays

MASR.A.49: distinguish between association and causation

MASR.A.50: ask if the difference between two population parameters (or two treatment effects) is due to random variation or if the difference is statistically significant

MASR.A.51: determine if there are significant differences between two population parameters or treatment effects

MASR.A.52: using simulation, determine the appropriate model to decide if there is a significant difference between two populations

MASR.A.53: using simulation, determine the appropriate model to decide if there is a significant difference between two treatment effects

MASR.A.54: understand that when randomness is incorporated into a sampling or experimental procedure, probability provides a way to describe the "long-run" behavior of a statistic as described by its sampling distribution

MASR.A.55: create simulated sampling distributions and understand how to use the sampling distribution to make predictions about a population parameter(s) or the difference in treatment effects

MASR.A.56: create an appropriate simulated sampling distribution (using technology) and develop a margin of error

MASR.A.57: create an appropriate simulated sampling distribution (using technology) and develop a alpha-value