Data Analysis & Descriptive Statistics

• Data analysis inspects, cleans, transforms, and interprets data to find relevant information.
• Data analysis is used to draw conclusions and support decision-making.

Types of Data

• Quantitative data is numerical and measurable, such as age, height and test scores.
• Qualitative data is non-numerical and describes qualities, such as colors, opinions and types of fruit.

Descriptive Statistics

• Descriptive statistics are used to summarize and describe the main features of a dataset.
• Mean is the average value of a dataset.
  • $Mean = \frac{\sum x_i}{n}$
  • $\sum x_i$ is the sum of all values.
  • $n$ is the number of values.
• Median is the middle value in a sorted dataset.
• Mode is the most frequently appearing value in a dataset.
• Standard Deviation measures the spread of data around the mean.
  • $\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}$
  • $x_i$ is each value in the dataset.
  • $\mu$ is the mean of the dataset.
  • $N$ is the number of values in the dataset.

Inferential Statistics

• Inferential statistics are used to make predictions or inferences about a population from a sample.
• Hypothesis Testing is a method to test the validity of a claim about a population.
• Confidence Intervals provide a range of values within which the true population parameter is likely to fall.
• Regression Analysis models the relationship between a dependent variable and independent variables.

Data Interpretation

• Data interpretation requires drawing conclusions based on data analysis results.
• Context involves understanding the conditions in which the data was collected.
• Limitations requires recognizing the constraints of the data and analysis methods.
• Implications necessitates identifying consequences of the findings for the research question.

Common Pitfalls

• Data Dredging involves analyzing data without a clear hypothesis, which can lead to spurious correlations.
• Confirmation Bias happens when interpreting data to confirm pre-existing beliefs.
• Overgeneralization is drawing broad conclusions based on limited data.

Software Tools

• Microsoft Excel is commonly used for basic data analysis and visualization.
• SPSS is a statistical software package used for advanced data analysis.
• R is a programming language for statistical computing and graphics.
• Python (with libraries like Pandas and NumPy) is versatile for data manipulation and analysis.