MIDTERMS REVIEWER.docx

**STATISTICS** -- science of **collecting, organizing, analyzing, interpreting, presenting data,** extraction of meaningful insight to make informed decisions **POPULATION** -- **complete set** of all possible observations/measurements of interest in a study, includes every individual/item that fit...

**STATISTICS** -- science of **collecting, organizing, analyzing, interpreting, presenting data,** extraction of meaningful insight to make informed decisions **POPULATION** -- **complete set** of all possible observations/measurements of interest in a study, includes every individual/item that fits the criteria being studied **SAMPLE** -- **subset of the population** selected for observation or measurement, used to make inferences about the population **VARIABLE** -- **any characteristic**, number, quantity measured or quantified, vary among individuals in population or sample **INDEPENDENT VARIABLE** -- variable **manipulated or controlled** in an experiment to determine its effect on a dependent variable (amount of sunlight is the independent variable) **DEPENDENT VARIABLE** -- variable that is **measured or observed** to determine the effect of the independent variable (growth of the plant is the dependent variable) **CONSTANT** -- variable that **doesn't change or vary**, remains the same throughout the study to ensure the effect of the independent variable is isolated (type of plant used, amount of water given is the constants) **DATA** -- values or observations collected during a study **TWO SCOPE** **DESCRIPTIVE STATISTICS** -- **summarizing, organizing data to describe** the sample or population (mean, median, mode, standard deviation) **INFERENTIAL STATISTICS** -- **making predictions or inferences** about a population based on a sample of data (hypothesis testing, confidence intervals, regression analysis **IMPORTANCE** **INFORMED DECISION MAKING** -- provide basis for making decisions based on data **IDENTIFYING TRENDS** -- reveal trends and patterns that are not immediately obvious **TESTING HYPOTHESES** -- test hypotheses and theories providing evidence for or against them **IMPROVING QUALITY** - used to monitor and improve product quality and process in manufacturing **NATURE OF STATISTICS** **QUANTITATIVE DATA** -- numerical data that can be **measured and compared** (height, weight, test scores) **QUALITATIVE DATA** -- categorical data that describes **attributes and characteristics** (gender, race, eye color) **LEVELS OF MEASUREMENT** **NOMINAL** -- categories **without a specific order** (blood type, gender) **ORDINAL** -- categories **with a specific order but without consistent difference** between categories (rankings, satisfaction levels) **INTERVAL** -- numerical data **with equal intervals but no true zero** (Celsius) **RATIO** -- numerical data with **equal intervals and a true zero** (weight) **EXAMPLE**: In a study evaluating the effectiveness of a new teaching method on student performance: **Population:** All students in the educational system. **Sample:** A group of 200 students from various schools. **Independent Variable:** The teaching method (traditional vs. new). **Dependent Variable:** Student performance (measured by test scores). **Data:** Test scores of students before and after implementing the new teaching method. **CATEGORICAL VARIABLES** -- variables that describes categories or groups **NUMERICAL VARIABLES** -- variables that describes quantities or amounts **METHODS OF DATA COLLECTION** **PRIMARY DATA COLLECTION** -- **original data** collected firsthand for specific research purpose, highly reliable and specific to the study needs - **EXPERIMENTS** -- controlled studies where **variables are manipulated to observe effects** - Pros -- high level of control - Cons -- expensive - **SURVEYS** -- **systematic collection of data** from a sample of individuals using **questionnaires or interviews** - Pros -- collect large data quickly and efficiently - Cons -- response bias, low response rate - **INTERVIEWS** -- direct, face-to-face interaction to collect **in-depth information** - Pros -- provides detailed rich qualitative data - Cons -- time-consuming, requires skilled interviewers - **OBSERVATIONS** -- systematic **recording of behavior or events** in a natural settings - Pros -- allows data collection in their natural setting - Cons -- subjective, may not capture all behavior - **FOCUS GROUPS** -- **guided group discussions** to explore perceptions and ideas on specific topics - Pros -- diverse perspectives, rich qualitative data - Cons -- group dynamics influence responses, not generalizable - **SECONDARY DATA COLLECTION** -- **use of existing data** collected for other purposes - **ARCHIVAL RESEARCH** -- use of **historical records**, documents to gather data - Pros -- cost-effective, time-saving - Cons -- outdated, not perfectly suited - **GOVERNMENT PUBLICATIONS** -- statistical reports, databases provided by **government agencies** - Pros -- reliable, comprehensive - Cons -- aggregated data - **ACADEMIC JOURNALS AND BOOKS** -- **published research** findings and reviews - Pros -- high-quality information - Cons -- access may be restricted **MIXED METHODS** -- **combining qualitative and quantitative methods** in a single study to leverage strengths of both approaches **SAMPLING** -- **selecting a subset of individuals** from a population to represent the whole **TYPES OF SAMPLING METHODS** **PROBABLITY SAMPLING** -- every member of the population has a **non-zero chance of being selected**, randomization, reducing bias - **SIMPLE RANDOM SAMPLING** -- every member of the population has an **equal chance of selection** - **EXAMPLE** -- drawing names from a hat to select participants for a study on consumer preferences - **STRATIFIED SAMPLING** -- divides population into **subgroups (strata)**, randomly samples from each - **EXAMPLES** -- dividing a population by age groups and then randomly selecting individuals from each age group for a health survey - **CLUSTER SAMPLING** -- divides the population, randomly selecting, sampling all individuals **in clusters** - **EXAMPLES** -- selecting several schools at a random from a district and surveying all students within those schools - **SYSTEMATIC SAMPLING** -- selecting **every n^th^ individual** from a list of population - **Examples** -- selecting every 10^th^ customer entering a store to survey shopping habits **NON-PROBABILITY SAMPLING** - **not all members of the population have a chance** of being included in the sample, does not rely on randomization, introduces bias - **CONVENIENCE SAMPLING --** sampling individuals who are **easily accessible** - Example -- surveying students in a classroom to understand study habits - **JUDGMENTAL/PURPOSIVE SAMPLING** -- selecting individuals based on a specific **criteria or judgement** - Example -- choosing expert practitioners for a study on advanced medical techniques - **SNOWBALL SAMPLING** -- **existing study subjects** recruit future subjects among their acquaintances - Example -- a study on a rare disease might start with a few know patients who then refer to others **METHODS OF DATA PRESENTATION** **TABULAR PRESENTATION** - **FREQUENCY TABLES** -- organizes data into **classes or categories** and shows the number of observations in each - **CROSS-TABULATIONS** -- displays the relationship between two or more variables by creating **a matrix format** **GRAPHICAL PRESENTATION** - **BAR CHARTS** -- used to compare **quantities** across **different categories** - **HISTOGRAMS** -- shows the **distribution of a dataset** and the **frequency of different intervals** - **PIE CHARTS** -- represents proportions of a **whole dataset** - **LINE GRAPHS** -- illustrates **trends over time** or sequential data - **SCATTER PLOTS** -- displays the **relationship** between **two continuous variables**, useful for identifying correlations **ADVANCED VISUALIZATION** - **BOX PLOTS** -- summarized data distributions showing **medians, quartiles, and outliers** - **HEAT MAPS** -- uses **color** to represent data density or frequency **in a matrix format** **Scenario 1: Statistical Analysis in a Study on a New Study Technique** A research team is investigating the effects of a new study technique on students\' academic performance. The study involves 500 high school students from various schools in a district. The team divides the students into two groups: one group uses the new study technique, while the other group continues with their regular study methods. After one semester, the team collects data on the students\' final exam scores and their reported study hours per week. **Key Terms:** - **Population:** All high school students in the district. - **Sample:** The 500 students who participated in the study. - **Independent Variable:** The type of study technique (New Technique vs. Regular Method). - **Dependent Variables:** Final exam scores and study hours per week. - **Constants:** Factors such as the duration of the study and the type of exams. **Scope and Importance:** - **Statistics\' Role:** Statistics helps determine whether the new study technique leads to higher final exam scores or different study habits compared to the regular method. By analyzing the data, researchers can make informed decisions about the effectiveness of the technique. **Classifying Data:** - **Group Assignment:** Categorical (Nominal). - **Final Exam Scores:** Numerical (Interval). - **Study Hours per Week:** Numerical (Ratio). **Scenario 3: Statistical Analysis of Class Size and Student Performance** A university conducts a study to assess the effect of class size on student performance. They collect data from 30 different classes of varying sizes. For each class, they record the number of students and the average final exam score of the class. They also gather data on the students\' major (e.g., Science, Arts, Business). **Key Terms:** - **Population:** All classes at the university. - **Sample:** The 30 classes studied. - **Independent Variable:** Class Size. - **Dependent Variable:** Average Final Exam Score. - **Constants:** Factors like the exam type or grading criteria could be considered constants if they remain the same across all classes. **Scope and Importance:** - **Statistics\' Role:** Statistics can analyze whether there is a correlation between class size and student performance by comparing average exam scores across different class sizes. This information could guide decisions on optimal class sizes to improve academic outcomes. **Classifying Data:** - **Class Size:** Numerical (Ratio). - **Average Final Exam Score:** Numerical (Interval). - **Student Major:** Categorical (Nominal)