Quantitative Research PDF

Descriptive Statistics Purpose and types, including central tendency, variability, and frequency distributions. Central Tendency Measures Explanation of mean, median, and mode, with examples. Variability Measures Range, standard deviation, and variance, focusing on when and why they...

Descriptive Statistics Purpose and types, including central tendency, variability, and frequency distributions. Central Tendency Measures Explanation of mean, median, and mode, with examples. Variability Measures Range, standard deviation, and variance, focusing on when and why they’re used. Frequency Distributions and Graphs Types (bar chart, histogram, frequency polygon) and how to interpret them. Bivariate Statistics Correlation (Pearson’s r), positive and negative correlations, and interpreting coefficients. Scatterplots and Regression Basics of predicting relationships between variables, using scatterplots and regression. Practical Application Tips How to apply these statistics to real-life data scenarios, using SPSS outputs as examples. Study Guide: Analyzing Quantitative Data 1. Descriptive Statistics Purpose: Used to describe, organize, and interpret data by identifying patterns and summarizing the main features. Key Types: ○ Measures of Central Tendency: Mean, median, mode. ○ Measures of Variability: Range, variance, standard deviation. ○ Frequency Distributions: Display data points to show how often they occur. ○ Data Distributions: Understanding data shape (e.g., normal or skewed).  2. Levels of Measurement - Determined by nature of thing being measured - Helps determine the type of statistics to be used - Critical thinking decision path shows relationship between measurement levels and descriptive statistics. Nominal - Variables are classified mutually - Dicho: true/false, male/female exclusive, no ranking - Categoricals: marital status may - Dichotomous variables have 2 true be married, divorced, widowed, values. single. - Categoricals have more than 2 true values. Ordinal - Relative rankings - 1. High School education → 2. Associate degree → 3. Bachelors Ordinal with - Gives difference with value 1. Highly disagree, 2. Disagree 3. interval - No = interval Neutral 4. Agree Interval - Ranks, with = intervals - 95-100, 101-106 Ratio - Highest level of measurement - Person weighing 20kg is twice - Absolute 0 as heavy as 10kg - Can divide, multiply - = interval 3. Measures of Central Tendency Central tendency measures help us find the "center" of a data set. Mean (Average): ○ Formula: Sum of all values ÷ Number of values. ○ Example: Data set = 5, 10, 15. Mean = (5 + 10 + 15) ÷ 3 = 10. ○ Sensitivity: Affected by extreme values (outliers), which can skew the mean. ○ Represented by M. n= sample size N= population size - Sample mean best represents population Median (Middle Value): ○ Definition: The middle value when data is ordered from least to greatest. ○ Usage: Median is preferred when data has outliers since it's less affected by extremes. ○ Example: For 3, 8, 10, 12, 15, the median is 10.  - Median is middle point in a set of cases, so extreme scores do not affect it. Mode (Most Frequent Value): ○ Definition: The most frequently occurring value in a dataset. ○ Example: In 1, 2, 2, 3, 4, the mode is 2. ○ Usefulness: Good for categorical data, but less useful in datasets without repeated values. - Least precise method 4. Measures of Variability Variability shows how much the data values differ from each other and the central tendency. Also what individual scores represent. Percentiles are values that divide a set of data into 100 equal parts. They indicate the relative standing of a particular data point within a dataset by showing the percentage of data points that fall below a given value. For example: If a student scores at the 75th percentile on a test, it means they scored higher than 75% of the other students. The 50th percentile is also known as the median and represents the middle of the dataset. Range: ○ Formula: Highest value – Lowest value. ○ Example: In a dataset 3, 7, 10, 15, 20, the range = 20 - 3 = 17. Standard Deviation (SD): ○ Definition: represents the average amount of variability from the mean ○ Importance: A larger SD means data points are spread out, a smaller SD means they are closer to the mean. ○ Example: The standard deviation or range indicates how spread out the values are. A larger standard deviation implies more variability around the mean. Variance: ○ Formula: Standard deviation squared (SD²). ○ Importance: Variance tells us how much the values in a dataset diverge from the mean and from each other. ○ When variance is low, the data points are clustered closely around the mean, suggesting consistency within the data. ○ When variance is high, the data points are more dispersed, indicating greater diversity or inconsistency within the dataset. 5. Frequency Distributions Frequency distributions show how often each value appears in the dataset. Tables: Organize scores in intervals (e.g., age groups). Graphs: ○ Bar Charts: Used for categorical data (nominal/ordinal). ○ Histograms: Used for continuous data (test scores)(interval/ratio). ○ Frequency Polygons: Connects data points to show distribution trends. ○ Why use a frequency polygon rather than a histogram to represent data? - Can simplify the interpretation of continuous data, smoother representation. 6. Shapes of Distributions The shape of a distribution helps to understand data patterns. Normal Distribution: ○ Symmetrical, bell-shaped curve where most data points cluster around the mean. Skewed Distributions: ○ Positive Skew: Tail on the right, data clusters around low values. ○ [median < mean] ○ Negative Skew: Tail on the left; occurs when data clusters around high values. ○ [median>mean] 7. Bivariate Statistics: Correlation Bivariate statistics examine relationships between two variables. Correlation Coefficient (r): ○ Measures the strength and direction of a relationship between variables. ○ Range: -1.00 to +1.00. Positive Correlation: Both variables increase or decrease together (e.g., study time and grades). Negative Correlation: One variable increases while the other decreases (e.g., exercise and weight). Interpreting Correlation Coefficients: ○ Strong Positive (e.g., r = +0.7): High correlation. ○ Weak Positive (e.g., r = +0.3): Low correlation. ○ Strong Negative (e.g., r = -0.8): Strong inverse relationship. 8. Scatterplots and Regression Scatterplots and regression help visualize and predict relationships between variables. Scatterplot: ○ A graph with data points representing two variables. Patterns (upward or downward trends) show correlation strength. Linear Regression: ○ Purpose: Predicts the value of one variable based on the value of another. ○ R is correlation coefficient. R2 is the coeff of determination. The rest is unexplained variance. ○ Regression Line: Line of best fit through the data points on a scatter plot. 9. Practical Tips and SPSS Outputs SPSS (Statistical Package for the Social Sciences) is often used for data analysis in research. Interpreting Outputs: ○ Descriptive Statistics: Check the mean, median, and SD to understand data spread. ○ Correlation Outputs: Look at r values to understand variable relationships. If both values decrease together, that indicates a positive correlation. If one value increases while the other decreases, that indicates a negative correlation. Correlation coefficients provide info about: - Associative relationship but not causal - Relationships between variables, how they change, or common A contingency table/ cross-tabulation table: - a two-dimensional frequency distribution shows how often two variables occur together. - relationship between two categorical or ordinal variables. - If you were analyzing gender (male/female) and preference for a product (like/dislike), a contingency table would show how many males and females liked or disliked the product. Summary 1. Understand: Descriptive statistics describe and summarize data. 2. Measure: Central tendency (mean, median, mode) and variability (range, SD, variance). 3. Visualize: Frequency distributions and graphs (bar, histogram, polygon). 4. Analyze Relationships: Correlation shows how variables relate. 5. Predict: Regression helps in making predictions based on data trends.