Go back

Course Page ✏️

Statistics - Economics with Data Science / Economics and Business

91983

Description

Course program
PART I
Random experiments, events, and probabilities. Sample space. Operations between events, relations between events. Three axioms. Some basic theorems. Conditional probability. Independence. Counting rules. Random variables. Discrete Random Variables and the Probability mass function. Expected value and variance. Bernoulli random variable. Binomial random variable. Expected value of a sum of random variables. Variance of a sum of independent random variables. Expected value and variance of the Binomial random variable. The Poisson random variable. Random experiments with an uncountable set of events. Continuous random variables. Density function. The Normal random variable, its shape and its density function. Expected value and variance of continuous random variables. Expected value and variance of the Normal rv. Standardization. Expected value and variance of a standardized random variable. Distribution of a standardized random variable. Distribution of a linear combination of a Normal random variable. The standardized Normal. Computing normal probabilities using the standardized Normal and "statistical tables". A random variable describes a population. A statistic as a random variable. Sampling distribution of a statistic. Sampling distribution of the sample mean. Sampling distribution of the sample proportion. Point and set estimation. Confidence interval for the population mean. Confidence interval for the population proportion. Computing the quantiles of a Normal distribution. Sum of random variables. Central Limit Theorem. The continuous Uniform distribution. Hypothesis testing. Null and alternative hypothesis. Rejection region. Critical values. First and second type error. Test level. Test for the mean when the variance is known (two tails). Test for the mean when the variance is unknown (two tails). Test for a proportion (two tails). One-tail Tests. Fisher and the p-value approach to testing. Potential Hypothesis-Testing Pitfalls and Ethical Issues. Pooled-Variance t Test for the Difference Between Two Means. Comparing the Means of Two Related Populations. Paired t Test. F-test for the Ratio of Two Variances. Chi-Square Test of independence. Chi-Square Test for differences among two or more proportions.
PART II
Introduction to statistical analysis: What is statistics all about? Detecting Patterns and Relationships Improper uses of statistics. Phases of a statistical survey Survey design and preliminary planning, Pretesting, Final survey design and planning, Data collection, Data cleaning, data-file construction, analysis, and final report. Reading the News. The educated consumer of data. Four hypothetical examples of bad reports. Planning your study. Measures, Mistakes and Misunderstandings. "Simple" measures don't exist. Defining what is being measured. 3.5 Defining a common language. How to get a good sample, research strategies. Defining a common language. Simple random sampling and other sampling methods. Difficulties and disasters in sampling. Experiments and Observational Studies. Designing a good experiment. Difficulties and disasters in experiments. Designing a good observational sxperiment. Difficulties and disasters in observational studies. Getting the Big Picture Organizing and visualizing data. Summarizing and Displaying Measurement Data. Turning data into information. Picturing data: histograms, pie charts, barplot and scatter. Numerical descriptive measures. Summary statistics. Bell-shaped Curves and Other shapes. Populations, frequency curves and proportions. Normal Curves. Percentiles and standardized scores. z-scores and familiar intervals. Well-designed statistical pictures. Pictures of categorical data. Pictures of measurements variables. Pictures of trends across time. Relationships between Measurement Variables. Statistical relationships. Strength vs. statistical significance. Correlation. Relationships can be deceiving: spurious correlations. Correlation does not imply causation. Relationships between categorical variables. Displaying relationships: Contingency tables. Statistical Significance for 2x2 tables. Measuring the strength of a relationship. Steps for assessing statistical significance. The chi-square test. Probability and long-term expectations. Probability. Relative frequency interpretation. Personal-probability interpretation. Some simple probability rules. When intuition differs from relative frequency. Revisiting personal probability. Coincidences. The gambler's fallacy. Confusion of the inverse. Using expected values to make wise decisions. Understanding the Economic news. Cost of living: The Consumer Price Index. Uses of the Consumer Price Index. Criticisms of the Consumer Price Index. Seasonal adjustments: Reporting the Consumer Price Index. Economic Indicators. Understanding and Reporting Trends over Time: what is a time series. A Time Series Plot, components of a time series, irregular Cycles and Random Fluctuations.

ECTS credits

Teaching Language

English

Exam Language

English

Support Materials Language

English

Basic Learning Outcomes

Identify and display univariate and bivariate data and interpret the graphs
(91983.1 - 91983.STATS.1 - BET - Identify and display univariate and bivariate data and interpret the graphs )
Calculate numerical summaries and interpret them to understand a given dataset
(91983.2 - 91983.STATS.2 - BET - Calculate numerical summaries and interpret them to understand a given dataset )
Discuss basic ideas of linear regression and correlation: create and interpret a line of best fit and calculate and interpret the correlation coefficient and the regression parameters
(91983.3 - 91983.STATS.3 - BET - Discuss basic ideas of linear regression and correlation: create and interpret a line of best fit and calculate and interpret the correlation coefficient and the regression parameters )
Distinguish and discuss sampling techniques, and distinguish between an observational study and a randomized experiment, including their effects on conclusions drawn
(91983.4 - 91983.STATS.4 - BET - Distinguish and discuss sampling techniques, and distinguish between an observational study and a randomized experiment, including their effects on conclusions drawn )
Distinguish between the apriori, empirical, subjective, and axiomatic approach to probability
(91983.5 - 91983.STATS.5 - BET - Distinguish between the apriori, empirical, subjective, and axiomatic approach to probability )
Calculate probabilities of events, including unions, intersections, complements, and conditional (using counting rules when needed)
(91983.6 - 91983.STATS.6 - BET - Calculate probabilities of events, including unions, intersections, complements, and conditional (using counting rules when needed) )
Use common probability distributions (discrete uniform, binomial, Poisson, continuous uniform, exponential, normal) to describe the behavior of random experiments, and identify likely and unlikely outcomes
(91983.7 - 91983.STATS.7 - BET - Use common probability distributions (discrete uniform, binomial, Poisson, continuous uniform, exponential, normal) to describe the behavior of random experiments, and identify likely and unlikely outcomes )
Manipulate probability distributions to produce new distributions (e.g., sum of random variables, standardization).
(91983.8 - 91983.STATS.8 - BET - Manipulate probability distributions to produce new distributions (e.g., sum of random variables, standardization).)
Recognize sample-to-sample variability and the existence of sampling distributions (e.g., of the mean and of the proportion), and the importance of the Central Limit Theorem in such a context.
(91983.9 - 91983.STATS.9 - BET - Recognize sample-to-sample variability and the existence of sampling distributions (e.g., of the mean and of the proportion), and the importance of the Central Limit Theorem in such a context.)
Construct and interpret in real context point estimates and confidence intervals to estimate population parameters (e.g., mean, proportion)
(91983.10 - 91983.STATS.10 - BET - Construct and interpret in real context point estimates and confidence intervals to estimate population parameters (e.g., mean, proportion) )
Describe potential Type I and II errors in a given setting, and explain how “not rejecting” the null hypothesis is different from “accepting” the null hypothesis, and the difference between statistical significance and practical importance in the context of a specific test of hypothesis and research question.
(91983.11 - 91983.STATS.11 - BET - Describe potential Type I and II errors in a given setting, and explain how “not rejecting” the null hypothesis is different from “accepting” the null hypothesis, and the difference between statistical significance and practical importance in the context of a specific test of hypothesis and research question.)
Conduct a hypothesis test about population parameters (e.g., mean, proportion) or differences between parameters (e.g., mean, variances) when given a research question and a clean set of data (after verifying that necessary conditions are met)
(91983.12 - 91983.STATS.12 - BET - Conduct a hypothesis test about population parameters (e.g., mean, proportion) or differences between parameters (e.g., mean, variances) when given a research question and a clean set of data (after verifying that necessary conditions are met) )
Upon completion of the course, students will have acquired a thorough understanding of the fundamental tools of univariate and bivariate descriptive statistics and inference. They will be able to calculate key statistical indices, make predictions (under certain conditions), and assess the significance of an estimate.
(91787.1 - 91787.STATS.1 - BET - Upon completion of the course, students will have acquired a thorough understanding of the fundamental tools of univariate and bivariate descriptive statistics and inference. They will be able to calculate key statistical indices, make predictions (under certain conditions), and assess the significance of an estimate. )

Final Learning Outcomes

Course categorized

Managing Entity (faculty)

Department of Economics and Law (UNICAS)