Page 9
Semester 3: Statistics for Behavioural Science
Basic Statistical Concepts - Variables, Scales, Measures of Central Tendency
Basic Statistical Concepts - Variables, Scales, Measures of Central Tendency
Variables
Scales of Measurement
Measures of Central Tendency
Organizing and Representing Data - Frequency Distribution, Graphs, Percentiles
Organizing and Representing Data
Frequency Distribution
Frequency distribution is a way to organize data so that it shows how often each value occurs. It can be represented in tabular format, providing a count of occurrences for each unique value in a dataset. This is useful for identifying trends and patterns in data. It can also be visualized using histograms or bar charts, which can help in understanding the distribution of data points.
Graphs
Graphs are visual representations of data that help in understanding patterns and relationships. Common types of graphs include bar graphs, line graphs, pie charts, and scatter plots. Each type serves different purposes, such as showing changes over time or representing parts of a whole. Graphs should be clear, well-labeled, and appropriately scaled to accurately convey the information.
Percentiles
Percentiles are used to describe the relative standing of a value within a data set. A percentile indicates the value below which a given percentage of observations fall. For example, the 25th percentile indicates that 25% of the data points are below that value. Percentiles are useful for comparing scores or measurements in different contexts, particularly in psychology and social sciences for standardized testing and assessments.
Parametric Analysis - Correlation, t Tests, ANOVA
Parametric Analysis - Correlation, t Tests, ANOVA
Introduction to Parametric Analysis
Parametric analysis refers to statistical techniques that assume a specific distribution for the data. It is commonly used when the data can be approximated by a normal distribution. These methods include correlation, t tests, and ANOVA.
Correlation
Correlation measures the relationship between two variables. It indicates how strongly the variables are related. The most common measure is Pearson's correlation coefficient, which ranges from -1 to +1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.
t Tests
t tests are used to compare the means of two groups to determine if they are significantly different from each other. There are different types of t tests, including independent samples t test and paired samples t test. The independent samples t test is used when two different groups are compared, while the paired samples t test is used when the same group is tested before and after a treatment.
ANOVA (Analysis of Variance)
ANOVA compares the means of three or more groups to see if at least one of the group means is different from the others. It is an extension of the t test and helps to avoid Type I errors when multiple t tests are performed. The most common type is one-way ANOVA, which analyzes one independent variable with multiple levels.
Assumptions of Parametric Tests
Parametric tests come with certain assumptions such as normality of data, homogeneity of variance, and independence of observations. It is essential to check these assumptions before applying these tests to ensure valid results.
Applications in Behavioral Science
These parametric methods are widely used in behavioral sciences to analyze experimental data, survey results, and observational studies. Understanding how to apply these techniques is crucial for drawing valid conclusions in psychological research.
Non-Parametric Analysis - Mann-Whitney U, Chi-square Tests
Introduction to Non-Parametric Analysis
Non-parametric analysis refers to statistical methods that do not assume a specific distribution for the data. These methods are particularly useful when data does not meet the assumptions required for parametric tests, such as normality.
Mann-Whitney U Test
The Mann-Whitney U Test is a non-parametric test used to compare differences between two independent groups. It evaluates whether the distribution of the ranks of the two groups differs significantly.
Assumptions of Mann-Whitney U Test
1. Two independent samples. 2. Ordinal, interval, or ratio scale of measurement. 3. The shape of the distribution does not need to be normal.
Chi-square Test
The Chi-square test is a non-parametric test used to determine if there is a significant association between categorical variables. It compares the observed frequencies in each category to the frequencies expected under the null hypothesis.
Types of Chi-square Tests
1. Chi-square test of independence - determines if there is a significant association between two categorical variables. 2. Chi-square goodness of fit test - checks if sample data matches a population with a specific distribution.
Assumptions of Chi-square Tests
1. Observations must be independent. 2. Categories should be mutually exclusive. 3. Expected frequencies should be adequate, typically at least 5.
Applications in Behavioral Science
Non-parametric tests like Mann-Whitney U and Chi-square are widely used in Behavioral Science to analyze data that do not meet parametric assumptions, facilitating research in psychology and social sciences.
Using Software - SPSS Data Entry, Analysis, Data Cleaning
Using Software - SPSS Data Entry, Analysis, Data Cleaning
Introduction to SPSS
SPSS is a powerful statistical software used for data management and analysis. It provides a user-friendly interface for researchers and analysts to perform complex statistical analyses without extensive programming knowledge.
Data Entry in SPSS
Data entry involves inputting raw data into SPSS. Users can enter data manually in the Data View or import data from various file formats such as Excel, CSV, or other statistical software.
Understanding Data Variables
In SPSS, data is organized into variables. Each variable has a name, type, and other properties like labels and values. Understanding variable types (nominal, ordinal, scale) is crucial for proper data analysis.
Data Cleaning in SPSS
Data cleaning is essential to ensure the integrity and accuracy of the dataset. Common tasks include identifying and handling missing values, correcting inconsistencies, and removing outliers to prepare the data for analysis.
Statistical Analysis Using SPSS
SPSS provides a wide array of statistical analysis options, including descriptive statistics, inferential statistics, regression analysis, ANOVA, and more. Users can perform analyses using dialog boxes or syntax.
Interpreting SPSS Output
After analysis, SPSS generates output in the form of tables and graphs. Understanding these outputs is critical for interpreting results accurately. Key elements include understanding p-values, confidence intervals, and effect sizes.
Exporting Results from SPSS
Researchers can export SPSS output to various formats such as PDF, Word, or Excel for sharing and reporting. Properly formatting the output is important for presentation purposes.
