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Questions and Answers
What is the characteristic of a nominal scale of measurement?
What is the characteristic of a nominal scale of measurement?
Give an example of a variable that can be measured on an interval scale.
Give an example of a variable that can be measured on an interval scale.
Temperature
Ordinal scale consists of a set of categories that are organized in an ________ sequence.
Ordinal scale consists of a set of categories that are organized in an ________ sequence.
ordered
In a ratio scale, a value of zero indicates a total absence of the variable being measured.
In a ratio scale, a value of zero indicates a total absence of the variable being measured.
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Match the scale of measurement with its description:
Match the scale of measurement with its description:
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What are the four methods of studying the truth?
What are the four methods of studying the truth?
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Which of the following define statistical concepts as observational versus experimental research and descriptive versus inferential statistics?
Which of the following define statistical concepts as observational versus experimental research and descriptive versus inferential statistics?
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Random sampling is not important in statistical analysis.
Random sampling is not important in statistical analysis.
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Parameter describes a _______ and Statistic describes a _______.
Parameter describes a _______ and Statistic describes a _______.
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Match the following measurement scales with their descriptions:
Match the following measurement scales with their descriptions:
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What is the sampling method that requires the selection of a starting point for the sample and sample size that can be repeated at regular intervals?
What is the sampling method that requires the selection of a starting point for the sample and sample size that can be repeated at regular intervals?
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What is stratified random sampling?
What is stratified random sampling?
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Cluster sampling divides the entire population into sections or clusters that do not overlap.
Cluster sampling divides the entire population into sections or clusters that do not overlap.
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___ sampling is a sampling technique wherein members of the sample are drawn from the population based on the judgement of the researcher.
___ sampling is a sampling technique wherein members of the sample are drawn from the population based on the judgement of the researcher.
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Match the sampling method with the appropriate description:
Match the sampling method with the appropriate description:
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What is the purpose of using non-probability sampling in research?
What is the purpose of using non-probability sampling in research?
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What are the steps expert researchers follow to decide the best sampling method?
What are the steps expert researchers follow to decide the best sampling method?
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What formula is used to determine the sample size from a given population size?
What formula is used to determine the sample size from a given population size?
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What is the minimum sample size that may be drawn for a survey on 5000 students of ABC College if an error of at most 5% is allowed?
What is the minimum sample size that may be drawn for a survey on 5000 students of ABC College if an error of at most 5% is allowed?
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Scores in a test are a ______ form of data.
Scores in a test are a ______ form of data.
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IQ scores are measured on a ______ scale of measurement.
IQ scores are measured on a ______ scale of measurement.
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Which type of data is self-esteem of senior high school students?
Which type of data is self-esteem of senior high school students?
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Descriptive statistics are used to make predictions based on current data.
Descriptive statistics are used to make predictions based on current data.
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In inferential statistics, what does a psychologist investigate to determine a significant relationship?
In inferential statistics, what does a psychologist investigate to determine a significant relationship?
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Study Notes
Introduction to Statistics
- Statistics refers to a set of mathematical procedures for organizing, summarizing, and interpreting information.
- It is a branch of mathematics that deals with the collection, organization, and interpretation of data.
Purpose of Statistics in Research
- Organize and summarize information to see what happened to the research study.
- Communicate the results to others.
- Answer general questions that initiated the research by determining exactly what conclusions are justified based on the results obtained.
Population and Samples
- Population: The set of all individuals of interest in a particular study, denoted by N.
- Sample: A set of individual selected from a population, usually intended to represent the population in a research study, denoted by n.
- Relationship between a population and a sample: a sample is a subset of the population.
Parameters and Statistics
- Parameter: A numerical value that describes a population, obtained from the population.
- Statistic: A numerical value that describes a sample, an estimate of a parameter, obtained from a sample.
Variables and Data
- Variable: A characteristic or condition that changes or has different values for different individuals.
- Data: Measurements or observations, facts or set of information or observation under study.
- Classification of variables:
- Discrete Variables: consists of separate, indivisible categories.
- Continuous Variables: has an infinite number of possible values that fall between any two observed values.
- Classification of data:
- Metric Data: data obtained by measurement.
- Enumeration Data: data obtained by counting.
- Categorical Data: data which can be classified into groups or categories of responses.
Scales of Measurement
- Nominal Scale: consists of a set of categories that have different names, used for identification purposes.
- Ordinal Scale: consists of a set of categories that are organized in an ordered sequence, used to rank observations.
- Interval Scale: has an arbitrary zero point, used to specify the amount of difference.
- Ratio Scale: anchored by a zero point that is not arbitrary, used to specify the amount of difference.
Statistical Notations
- Descriptive Statistics: used to summarize, organize, and simplify data.
- Inferential Statistics: used to make generalizations about a population from a sample.
Sampling Error
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Sampling Error: the discrepancy between a sample statistic and the corresponding population parameter.
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Margin of Error: the maximum likely size of the sampling error when the sampling is random.### Sampling Techniques
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Bias in sampling can occur due to various reasons, such as: • Bias in choosing samples • Typographical errors or wording used in questionnaires • Undesirable answers in surveys or polls • Low response rates
Probability Sampling
- Definition: A sampling technique where each member or element of the population has an equal chance of being selected as a member of the sample.
- Assumptions: • The researcher has a complete list of the members of the population. • The selection of members of the sample is not predetermined.
- Characteristics: • Sampling without bias • Every member of the population has an equal opportunity to be part of the sample
- Techniques: • Simple Random Sampling (SRS) • Systematic Sampling • Stratified Sampling • Cluster Sampling • Multi-Stage Sampling
Simple Random Sampling (SRS)
- Definition: A technique of drawing a sample where each element of the population has an equal chance of being taken into the sample.
- Characteristics: • The most basic form of probability sampling • Unbiased • Saves time and resources
- Example: Lottery, Table of Random Digits
Systematic Sampling
- Definition: A technique of choosing an element for every k elements of a population.
- Characteristics: • Easy to implement • Time-efficient • Requires a starting point and sample size
- Example: Choosing every 10th individual from a population of 5000
Stratified Sampling
- Definition: A technique of dividing a population into groups (strata) and sampling is done in each stratum.
- Characteristics: • Ensures representation of the entire population • Can be used for both equal and proportional allocation
- Example: Dividing a population of 1000 families into high, average, and low socio-economic status groups
Cluster Sampling
- Definition: A technique of taking a sample from groups, and all the elements in those groups are chosen.
- Characteristics: • Identifies clusters based on demographic parameters • Simple and cost-effective
- Example: Dividing the US into states (clusters) to evaluate the number of immigrants
Multi-Stage Sampling
- Definition: A sampling technique in various stages until the desired sampling units are obtained.
- Characteristics: • Used for large-scale studies • Allows for flexibility in sample selection
Non-Probability Sampling
- Definition: A sampling technique where members of the sample are drawn from the population based on the judgment of the researcher.
- Characteristics: • Lacks objectivity • Results are relatively biased • Not suitable for making inferences about a population
- Techniques: • Convenience Sampling • Purposive Sampling • Snowball Sampling • Quota Sampling
Convenience Sampling
- Definition: A technique of selecting samples based on ease of access to subjects.
- Characteristics: • Used for pilot studies or exploratory research • Limited to no prior information available • Time-efficient and cost-effective
Purposive Sampling
- Definition: A technique of choosing sampling units from a given population with specific characteristics.
- Characteristics: • Used for studying specific populations or groups • Selection is based on the researcher's discretion
Snowball Sampling
- Definition: A technique of tracking a few categories to interview and derive results.
- Characteristics: • Used for difficult-to-reach populations • Used for sensitive topics
Quota Sampling
- Definition: A technique of setting a sample size based on the nature of the data needed.
- Characteristics: • Used for rapid collection of samples • Selection is based on pre-set standards
Determining Sample Size
- Formula: n = 1 / (1 + Nα^2)
- Where: • n = sample size • N = population size • α = level of significance (allowable error)
- Example: Calculating the minimum sample size for a survey of 5000 students with an error of at most 5%.### Psychological Statistics
Scales of Measurement
- Nominal scale: used to label or categorize data, e.g. religion, civil status, address
- Ordinal scale: used to rank data, e.g. IQ scores, size of a T-shirt
- Interval scale: used to measure data with equal intervals, e.g. speed of a car, temperature
- Ratio scale: used to measure data with a true zero point, e.g. land area, salary of workers
Descriptive vs. Inferential Statistics
- Descriptive statistics: used to describe and summarize existing data, e.g. computing the average grade of students, counting furniture in a school
- Inferential statistics: used to make predictions or inferences about a larger population based on a sample, e.g. predicting future sales, investigating the relationship between mental age and chronological age
Sample Size
- Errors in sample size: 1% error, 2.5% error, 5% error, 7.5% error, 10% error
- Formula for determining sample size: depends on population size and desired error margin
Presentation of Data
- Frequency distribution table: a table that displays the frequency of each value or range of values in a dataset
- Types: simple, complete, relative, cumulative, cumulative percentage
- Graphs: used to visualize data
- Types: bar chart, histogram, frequency polygon, pie chart, ogive
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Description
Start your synchronous learning journey with this module, which introduces the fundamental concepts of statistical analysis in psychology.
