Lecture_1_STATS

Introduction to Statistics

• Statistics: The science of planning studies and experiments to obtain data, organizing, summarizing, presenting, analyzing, and interpreting the data to draw conclusions that inform decisions.

Types of Statistics

• Descriptive Statistics: Methods of organizing, displaying, and describing data using tables, graphs, and summary measures. Focused primarily in chapters 1-3.

• Inferential Statistics: Methods that use sample results to make decisions or predictions about a population. Introduced from chapter 6 onwards.

• Probability: Discussed in chapters 4 and 5, dealing with various distribution types (e.g., discrete and continuous).

Key Vocabulary

• Data: Collection of observations, such as measurements or survey responses (e.g., age, gender).

• Population: Complete collection of all measurements or data being considered.

• Census: The collection of data from every member of a population, conducted every ten years in the U.S.

• Sample: A subcollection of members selected from a population, used when full census is impractical.

• Sampling: The act of collecting data from a selected portion of a population.

Example Illustration

• ELAC Students:

  • Population: All ELAC students.

  • Sample: 200 ELAC students surveyed for age information.

Key Elements in a Statistical Study

1. Preparation: Identifying data, goals, and source of data.

2. Analysis: Using statistical methods to explore the data.

3. Conclusion: Drawing findings based on analysis.

Preparation Details

• What data means and the goal of the study. For example, assessing the relationship between pleasure boats and manatee fatalities in Florida:

  • Goal: Determine if a correlation exists between boat numbers and manatee fatalities.

  • Source: Credible data sources like the Florida Department of Highway Safety.

  • Sampling Method: Assessing whether the method used to collect data was biased.

Analysis Steps

• Graphing Data: Proper representation of results to avoid misleading conclusions.

• Outliers: Identify data points significantly different from others.

• Distribution: Assess if the data follows a normal distribution or others (e.g., binomial).

Conclusions

• Statistical Significance: A result unlikely to occur by chance (usually <5% probability).

  • Example: Getting 98 girls from 100 births is statistically significant.

• Practical Significance: Whether the findings have real-world relevance or worth considering.

  • Example: Weight loss of 2.1 pounds in a year may not hold practical significance for many individuals.

Distinction between Statistical and Practical Significance

• An outcome can be statistically significant but not practically significant; for example, slight improvements in treatments may not be worth the cost.

  • Example from ProCare Industries: Suggests a treatment that increases the chance of a baby girl from 50% to 52% is statistically significant but not worth the investment due to its trivial practical significance.

Potential Pitfalls in Making Conclusions

• Misleading Conclusions: Correlation does not imply causation; data should be measured accurately rather than reported biases.

• Small Sample Size: Avoid basing conclusions on a small sample.

• Loaded Questions: Ensure survey questions are unbiased and not leading respondents towards a specific answer.

Examples in Context

1. Self-selected Samples: Survey results from voluntary responses can skew results and represent a non-generalizable population.

2. Misleading Questions: The order and wording of survey questions can significantly impact responses.

3. Correlation vs. Causation: It’s essential to differentiate between a correlation observed in data and an actual cause-effect relationship.

Summary of Learning

• Statistics involve not just calculations but also interpretation to apply findings effectively. Understanding the significance and preparation, analysis, and conclusion steps is critical for sound statistical practice.