stats

• Statistics is a field of mathematics associated with numbers and figures, used for organizing, summarizing, and interpreting information
• In the behavioral sciences, statistics is used to assess and evaluate research results, helping researchers organize information and answer research questions
• Population: set of all individuals of interest in a study

  Sample: smaller group selected from the population, should be representative of the population
• Statistics analyze information from the sample to answer research questions and generalize results back to the population
• Variables: characteristics that change or have different values for different individuals

  Data: measurements or observations, data set is a collection of measurements
• Parameters: characteristics that describe a population

  Statistics: characteristics that describe a sample
• Descriptive statistics: summarize, organize, and simplify data

  • Measures of central tendency
  • Measures of variability
  • Measures of relative position
• Inferential statistics: techniques to study samples and generalize about populations

  • Hypothesis testing
  • ANOVA
  • Regression analysis
  • Chi-square
• Sampling error: discrepancy between a sample statistic and the corresponding population parameter

  • Naturally occurring error that exists between a sample and a population
• Constructs: internal characteristics that cannot be directly observed

  Operational definition: defines a construct in terms of external behaviors that can be observed and measured
• An operational definition identifies a measurement procedure for measuring an external behavior and uses the resulting measurements as a definition and a measurement of a hypothetical construct
• Operational definitions have two components:

  • Describing a set of operations for measuring a construct
  • Defining the construct in terms of the resulting measurements
• Discrete variables consist of separate, indivisible categories with no values between neighboring categories
• Examples of discrete variables include the number of children in a family or the number of students attending class
• Continuous variables like time, height, and weight are not limited to fixed categories and can be divided into an infinite number of fractional parts
• Continuous variables have an infinite number of possible values between any two observed values
• Real limits are boundaries of intervals for scores on a continuous number line, separating two adjacent scores exactly halfway between them
• Continuous and discrete apply to the variables being measured, not to the scores obtained from the measurement
• Descriptive research describes individual variables as they exist naturally
• The correlational method examines the relationship between two variables as they exist naturally for a set of individuals
• The experimental method compares groups of scores and aims to establish cause-and-effect relationships between variables
• In the experimental method, manipulation involves changing the value of one variable, while control ensures other variables do not influence the relationship being examined
• Participant variables and environmental variables are two categories that researchers must consider to control extraneous variables in experiments
• Experimental Method:

  • Involves the manipulation of the independent variable by the experimenter
  • The independent variable is the treatment conditions to which participants are assigned
  • Example: Amount of violence in a video game as the independent variable
  • The dependent variable is observed and measured to obtain scores within each condition
  • Example: Level of aggressive behavior as the dependent variable
• Frequency distribution is an organized tabulation of score values and their frequency of occurrence
• In behavioral research, the independent variable usually consists of the treatment conditions to which subjects are exposed
• It takes a disorganized set of scores and places them in order from highest to lowest, grouping together individuals who all have the same score
• Dependent Variable:

  • The variable observed to assess the effect of the treatment
  • In example 1, the level of aggressive behavior is the dependent variable
• A frequency distribution can be structured as a table or a graph, presenting the set of categories or scores and the frequency of individuals in each category
• Nonexperimental Method:

  • Compares groups without control over the groups
  • Examples include comparing different age groups, people with and without disorders, and children from different family structures
• In an ungrouped frequency distribution table, data is arranged from lowest to highest, showing the frequency of occurrence of different values
• Before and after studies are examples of nonexperimental methods

  • Changes in scores after an event can be due to the event or other factors beyond the researcher's control
• Scales of Measurement:

  • Involve assigning individuals or events to categories
  • Categories make up a scale of measurement, highlighting limitations and guiding statistical analysis
• Steps for creating an ungrouped frequency distribution table:

  1. Make 2 columns for scores (S) and frequency (f)

  2. List scores from highest to lowest

  3. Count the number of each score for the frequency column

  4. Calculate the total number of individuals (N) by adding all values in the frequency column
• Nominal Scale:

  • Involves classifying individuals into categories with different names
  • Categories do not have a quantitative relationship
  • Examples include race, gender, or occupation
• Ordinal Scale:

  • Categories have different names and are organized in a fixed order
  • Rankings imply a directional relationship between categories
• Interval and Ratio Scale:

  • Consist of ordered categories with equal intervals
  • Interval scale has an arbitrary zero point, while a ratio scale has a meaningful zero point
• Example of an ungrouped frequency distribution table:

  S (Scores) | f (Frequency)

  4 | 1

  6 | 2

  7 | 3

  8 | 7

  9 | 5

  10 | 2

  ∑f = 20
• In a grouped frequency distribution table, data is organized into class intervals showing the frequency of values within each interval
• Steps for creating a grouped frequency distribution table:

  1. Determine the range (highest - lowest score)

  2. Calculate the number of class intervals (k) using Sturge’s rule

  3. Determine the class width (i) by dividing the range by the number of class intervals

  4. Create class intervals starting from the lowest score

  5. Make columns for class intervals and frequency

  6. Tally the frequency for each class interval

  7. Calculate the cumulative frequency (cf) by adding frequencies from the lowest to the current class interval