ch 1

INTRODUCTION TO STATISTICS AND FREQUENCY DISTRIBUTIONS

READING QUESTIONS

  • Reading Question 1: Reading with purpose means:

    • a. Thinking about other things while reading.

    • b. Actively extracting information as you read.

  • Reading Question 2: It is better to:

    • a. Read the paragraph and then answer the question.

    • b. Read the question and then search for the answer.

  • Emphasize understanding when working on activities; figuring out errors reinforces learning.

  • Resist the urge to rush for correct answers; understanding is more important.

MATH SKILLS REQUIRED IN THIS COURSE

  • Basic math skills necessary: addition, subtraction, multiplication, division, squaring numbers, and taking square roots.

  • Familiarity with basic algebra is essential; for example, solving X^2 = 66 leads to X = 11.33 or X = -11.33.

  • Order of operations:

    1. Operations in parentheses.

    2. Exponents.

    3. Multiplication or division.

    4. Addition or subtraction.

  • Example of order application: In (3 + 4)^2 , first calculate 3 + 4 = 7 , then square to get 49 .

STATISTICAL SOFTWARE OPTIONS

  • Statistical analysis requires software or calculators. Use these mathematical foundations to inform computational choices.

  • Recommended software includes:

    1. IBM SPSS Statistics: Point-and-click interface but high cost and may be challenging for off-campus access.

    2. R (r-project.org): Free but requires coding expertise.

    3. JASP (jasp-stats.org) and Jamovi (jamovi.org):

      • Both are free and user-friendly point-and-click interfaces.

      • They offer different statistical capabilities compared to SPSS.

COMPARISON OF SOFTWARE:

Software

Features

Cost

JASP

Easy point-and-click interface

Free

Jamovi

Similar to JASP, intuitive interface

Free

SPSS

Expensive, complex setup

$$$

R

Flexible coding required

Free

WHY DO YOU HAVE TO TAKE STATISTICS?

  • Many academic majors require a statistics course: business, economics, nursing, political science, pre-medicine, psychology, social work, sociology.

  • Primary reason: informed decision-making relies on data—example:

    • Psychologists use statistics to evaluate treatment efficacy to avoid harming individuals.

THE FOUR PILLARS OF SCIENTIFIC REASONING

  1. Hypothesis Testing with a Continuous p value:

    • A formal multiple-step process for evaluating null hypotheses, also known as significance testing.

  2. Practical Importance with Effect Sizes:

    • Describes the magnitude of a study’s results enabling practical significance assessment.

  3. Population Estimation with Confidence Intervals:

    • Estimations of which values might exist in a population based on sampling variability.

  4. Research Methodology and Scientific Literature:

    • Understanding the context of statistical findings is critical for accurate interpretation and application.

  • Use multiple types of evidence to construct sound scientific conclusions, minimizing decision-making errors due to sampling variation.

POPULATIONS AND SAMPLES

  • Population: The full group sharing specific traits (e.g., all individuals with depression).

  • Sample: A selected subset of the population from which data is collected for inferential statistics.

  • Inferential statistics: Using sample data to estimate population parameters, accounting for the inherent sampling error.

SCALES OF MEASUREMENT

  1. Nominal Scale: Categorizes data into distinct groups with no order.

    • Example: types of depression.

  2. Ordinal Scale: Ranks data in order but does not specify the distance between entries.

    • Example: severity of depression (mild, moderate, severe).

  3. Interval Scale: Quantifies the distance between values where intervals are equal, but zero does not imply absence.

    • Example: temperature scales.

  4. Ratio Scale: Quantifies distance with an absolute zero indicating absence.

    • Example: annual income.

CLASSIFICATION EXAMPLES

  • Ordinals: depression categories; Interval: standardized test scores; Ratio: income measured in dollars; Nominal: types of pet ownership.

DISCRETE VS. CONTINUOUS VARIABLES

  • Discrete Variable: Measured in whole numbers (e.g., number of siblings).

  • Continuous Variable: Measured in fractions (e.g., weight in pounds).

GRAPHING DATA

  • Graphing is crucial for data interpretation.

    • Types of graphs:

    1. Bar Graphs: Used for nominal or discrete data where bars do not touch.

    2. Histograms: Used for continuous data with touching bars illustrating data distribution dense areas.

    3. Line Graphs: Similar to histograms but with connecting points.

SHAPES OF DISTRIBUTIONS

  • Normal Distribution: Bell-shaped and symmetrical, consists of most frequent scores at the center, tapering off towards the extremes.

  • Skewness: Differentiates between positively skewed (right tail longer) and negatively skewed (left tail longer) distributions.

  • Kurtosis: Indicates the peak of the distribution:

    • Leptokurtic: High peak.

    • Platykurtic: Flat peak.

FREQUENCY DISTRIBUTION TABLES

  • Used to organize raw data into a clear format to observe distribution patterns.

    • Example: Responses to customer satisfaction surveys structured to display frequency and percentage.

  • Percentile Calculation: Measures the position of a score relative to others in the distribution.

SAMPLE ACTIVITY

  • Analyze Milgram's obedience study with special attention to statistical methodologies and findings. Evaluate predictions made by outsiders versus actual outcomes observed.

ADDITIONAL STATISTICAL MEASURES

  • Consider various methodologies and their implications for interpreting results through the lens of ethical considerations.