Essential Statistics Concepts and Formulas
Fundamental Statistical Definitions
1. Define Mean: Mean is the average. It is calculated as the Sum of all values ÷ Number of values.
2. Find Mean of First Ten Natural Numbers: The first 10 natural numbers are 1 to 10. The sum is 55. Mean = 55 ÷ 10 = 5.5.
3. Define Median: The Median is the middle value when data is arranged in ascending or descending order.
4. Find Median of First Ten Even Numbers: The first 10 even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. For an even count (10 values), the
Read MoreAdvanced Statistical Analysis and Econometrics in SPSS
Skewness and Kurtosis: Distribution Shapes
What They Measure
- Skewness measures the asymmetry of a distribution around its mean.
- Positive (right) skew: Long right tail—most observations are on the left (e.g., income).
- Negative (left) skew: Long left tail—most observations are on the right.
- Skewness = 0: Symmetric distribution (ideally normal).
- Kurtosis measures tailedness and peakness—how heavy the tails are relative to a normal distribution.
- Mesokurtic: Kurtosis ≈ 3 (normal distribution).
- Leptokurtic:
Quantitative Versus Qualitative Research Methods Comparison
Elements of Investigation: Quantitative vs. Qualitative
1. Environment (MARCO)
- Quantitative: Can be developed in a natural environment or a closed laboratory.
- Qualitative: In contact with the object being studied, in a natural setting.
2. Design Structure
- Quantitative: Requires a fixed design established a priori (in advance).
- Qualitative: Has an emergent design; it is not fixed in advance.
3. Goals and Flexibility
- Quantitative: Techniques are pre-set, aiming for technical flexibility.
- Qualitative: The reality
Statistical Test Interpretation and SPSS Decision Rules
Statistical Significance: The Main Rule
The decision rule for hypothesis testing is based on the p-value:
- p < 0.05: Significant → Reject H0 (Null Hypothesis)
- p ≥ 0.05: Not significant → Fail to reject H0
Choosing the Appropriate Test:
- 1 group vs known value → One-Sample T-Test
- 2 groups (different people) → Independent Samples T-Test
- 2 groups (same people before/after) → Paired Samples T-Test
- 3+ groups → ANOVA (+ Tukey Post-Hoc if significant)
- Numeric ↔ Numeric relationship → Correlation
- Predict
Essential Data Science Concepts and Statistical Measures
Foundational Concepts in Data Science and Statistics
Essential Data Science Terminology
The following terms represent fundamental concepts used in data analysis and machine learning:
- Data Science: A field that uses scientific methods, algorithms, and tools to extract knowledge and insights from data.
- Datafication: The process of transforming information, activities, or objects into a data format.
- Population & Sample: The Population is the entire group being studied; the Sample is a representative
Essential Statistical Concepts for Data Analysis
Fundamentals of Business Statistics
Statistics Definition
The field concerning the collection, analysis, interpretation, and presentation of data used for the decision-making process in the business area.
Descriptive Statistics
Involves data collection methods, description, and summary data visualization. Focuses on the data as they are.
Inferential Statistics
The generation of models, inferences, and predictions associated with the phenomenon in question (predicting how the variable will behave).