Psychological Statistics Notes

Psychological Statistics with Renz Marion Gavino

Interesting Statistics

• As of 2021, the average life expectancy in the Philippines is approximately 71 years.

• 1 in 5 Filipinos experiences mental health issues in their lifetime.

• Only 1 in 5 individuals with mental health problems in the Philippines seeks treatment.

• Over 92% of the population now has access to clean and safe drinking water.

• A new advertisement for a popular ice cream brand led to a 30% increase in ice cream sales over the next three months, suggesting a positive impact on consumer demand.

• The statement that more churches in a city lead to more crime is presented with a caution against assuming causation.

• There are 75% more interracial marriages occurring this year than 25 years ago, suggesting increased societal acceptance of interracial marriages.

• It is noted that not everything read online, even with the prompt "psychology says…", is correct.

Statistical Procedures

• Learning Outcome: Equip students with the tools and techniques needed to analyze, interpret, and draw meaningful conclusions from data, enabling them to make informed decisions and contribute to evidence-based practices in the field of psychology.

• Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

• It involves using various methods to summarize and draw conclusions from data sets, helping to identify patterns, relationships, or trends.

• Statistics is the language of science and data.

Population

• A population is the set of all the individuals of interest in a particular study.

• A researcher may want to know what factors are associated with academic dishonesty among college students.

• A researcher may want to examine the amount of time spent in the bathroom for men compared to women.

• Because populations tend to be very large, it is usually impossible for a researcher to examine every individual in the population of interest.

Sample

• A sample is a set of individuals selected from a population, usually intended to represent the population in a research study.

• Samples can vary in size. For example, one study might examine a sample of only 10 students in a graduate program, and another study might use a sample of more than 10,000 people who take a specific cholesterol medication.

Variables

• Variables are characteristics or conditions that change or have different values for different individuals.

• Independent Variable: The variable in an experiment that is systematically manipulated by the investigator.

• Dependent Variable: The variable in an experiment that the investigator measures to determine the effect of the independent variable.

Data

• A datum (singular) is a single measurement or observation and is commonly called a score or raw score.

• Data (plural) are measurements or observations.

• A data set is a collection of measurements or observations.

• Discrete Data: Data that can take only specific values within a range. These values are countable and usually represent whole numbers.
  Operations: Can be counted but not divided into smaller parts.
  Values: Can only take whole numbers or integers.
  Examples: Number of children in a family, number of cars in a parking lot, number of books on a shelf.

• Continuous Data: Data that can take any value within a range and is measurable. It can take on an infinite number of values within a given interval.
  Operations: Can be measured and expressed with infinite precision (e.g., 2.34567).
  Values: Can take any value within a given range, including decimals or fractions.
  Examples: Height of a person (e.g., 5.6 cm, 5.75 cm), weight, temperature (e.g., 20.5°C), time taken to complete a task.

• Categorical Data: Data that represents categories or labels, which are typically non-numeric. It involves grouping items based on characteristics. Qualitative data representing different categories or groups.
  Operations: Can be used for classification or labeling, but no meaningful arithmetic operations like addition or subtraction.
  Values: Can take values representing different categories, but no inherent order (nominal) or with a natural ranking (ordinal).
  Examples: Gender (Male/Female), hair color (Black/Blonde/Red), marital status (Single/Married), favorite fruit (Apple/Orange/Banana).

• Countable: You can count it in whole numbers (like 1, 2, 3).

• Measurable: You can measure it and get values with decimals (like 5.25, 3.5).

• Data Measurement Criteria:

  • Is the data countable or measurable?

    • Discrete: Countable

    • Continuous: Measurable

    • Categorical: Neither

  • Can the data take any value, including fractions or decimals?

    • Discrete: No

    • Continuous: Yes

    • Categorical: No

  • Does the data represent categories or labels?

    • Discrete: No

    • Continuous: No

    • Categorical: Yes

Scales of Measurement

• Ratio scales have equal intervals between adjacent scores on the scale and an absolute zero.

• Interval scales have equal intervals between adjacent scores but do not have an absolute zero.

• Ordinal scales have some sort of order to the categories (e.g. in terms of magnitude) but the intervals between adjacent points on the scale are not necessarily equal.

• Nominal scales consist of categories that are not ordered in any particular way.

Criteria for Scales:

• Examples of Scales:

  • Nominal: Favorite color (red, blue, green), Car brands (Toyota, Ford, BMW), Pets (dog, cat, hamster), Fruit types (apple, banana, orange).

  • Ordinal: Movie ratings (1 star, 2 stars, 3 stars, 4 stars, 5 stars), Spicy food levels (mild, medium, hot, extra hot), Clothing sizes (small, medium, large), Ranking of sports teams (1st place, 2nd place, 3rd place).

  • Interval: Temperature (Celsius/Fahrenheit) (10 °C, 20 °C, 30 °C), Time on a clock (2:00 PM, 3:00 PM, 4:00 PM), Calendar years (2020, 2021, 2022).

  • Ratio: Height (0 cm, 100 cm, 200 cm), Weight (0 kg, 50 kg, 100 kg), Money ($0, $10, $100), Distance (0 meters, 5 meters, 10 meters).

• Interval vs Ratio:

  • A 1-10 effectiveness scale lacks an absolute zero and is interval data.

  • If the scale only ranked effectiveness levels (e.g., Poor, Average, Excellent), it would be ordinal.

• A true zero in a ratio scale means the complete absence of what is being measured.

• Sleep is a biological function that fluctuates and cannot be completely absent forever, it does not qualify as ratio data. Therefore a report of "0 hours of sleep," does not mean they permanently lack the ability to sleep or that sleep is an absolute quantity that can be "absent" in the same way as weight or money.

Parameter and Statistic

Descriptive vs. Inferential Statistics

• Example of what could go wrong:

  • A university wants to measure overall student satisfaction but only surveys 200 students out of 10,000.

  • Potential biases include overrepresentation of honors students, underrepresentation of freshmen and transfer students, most respondents being from one department, and the survey being conducted only in the library.

Sampling Procedures

Probability Sampling

• Random Selection: Used to ensure every individual has an equal chance of being selected, increasing generalizability.

NONProbability Sampling

• NON Random Selection: Not all individuals have an equal chance of being selected. Often used when random selection is not feasible.

When to Use Random vs. Non-Random Sampling