Measurement Scales, Statistical Concepts, and Research Methods in Social Sciences
Measurement Scales
Likert Scales
An ordinal level measurement of a person’s attitude, typically using a 5-7 point scale, allowing participants to indicate how much they agree or disagree with a statement. This method assumes that attitudes can be measured and ranked. It uses ordinal data with two extreme points and a neutral point, making it simple to complete.
Continuous Measurement Scale
Allows for fractional amounts/decimals, which make sense in this context.
Discrete Scale
Only fixed amounts can be measured and cannot be broken into smaller amounts.
Measurement Scale Summary
- Nominal (label/tags): Qualitative. No equal unit of measurement, no true zero. Example: Identifying males/females as 1 and 2, telephone numbers.
- Ordinal (groups variables in ordered categories): Relative quantity, no equal unit of measurement, no real zero. Used to judge order, such as 1st, 2nd, etc., in a race or school grades.
- Interval (equal distance between objects): Quantitative. Equal unit of measurement, no real zero. Used to convey the results of intelligence and personality tests, individuals’ standing relative to class average.
- Ratio (fixed measurement): Quantitative. Equal unit of measurement, true zero exists. Used to count the number of correct answers on a test, distance traveled.
Central Tendency
(What is normal or average for a set of data)
- Mode: The most reoccurring value.
- Median: The middle value when arranged from least to greatest (e.g., in a set of numbers from 1-10, the median is 5.5).
- Mean: The average of all values.
Frequency Distribution
Summarizes nominal/ordinal levels in a table (f/ by total entire sample count x 100).
Grouped Frequency Distribution
Organizing a large set of data into manageable groups (class intervals/must not overlap).
Guidelines
- Logically defensible
- Exclusive
- First interval lowest, last interval highest
- Same width
- 7-13 intervals
Descriptive Statistics (Graphs)
Frequency distribution shows scores on the x-axis & their frequency on the y-axis.
- Bar Graph: (Nominal/ordinal categorical) height shows frequency.
- Histogram: (Ratio/interval continuous).
Normal Distribution
A bell-shaped curve where the far left/right shows low frequency. Extreme high/low values are called tails of the distribution. Data near the mean are more frequent.
A normal distribution has a mean of 0 and a standard deviation of 1. Each deviation corresponds to a Z-score. Example: If the mean of a data set is 50 and the standard deviation is 10, a data point with a value of 60 would have a Z-score of 1 (since it is 1 standard deviation above the mean), while a data point with a value of 40 would have a Z-score of -1 (since it is 1 standard deviation below the mean).
Variance and Standard Deviation
(Finds the spread; is it expected or significant?)
Indicate how dispersed the data is in relation to the mean. Low deviation data is clustered around the mean, while large variance data is spread out. These measures require interval/ratio data and are the most used. They are based on the distance of each score from the mean of the distribution, with the mean as the reference point. Example: The class average on a stats test was 72, with a standard deviation of 3.6. What is the score 2 SD above the mean? 79.2. Example: In a normal distribution, what percent of scores are within +/- standard deviation of the mean?— 68.
Probability and the Normal Curve
Statistics tell us the probability that an event will occur. Probability allows us to make inferences about a population based on sample data. Probability theory is the foundation of inferential statistics, attempting to estimate the chance that an event will occur.
Probability and the Normal Curve: Z-Scores
- Using the normal curve as a probability distribution allows us to predict areas under the curve.
- 68-95-99.7% rule for standard deviations under the curve.
- Scores under a normal curve can be transformed into z-scores.
- Z-scores indicate how far above or below the mean the score is in units of standard deviation.
- Positive scores fall above the mean, and negative scores fall below the mean.
- Example: If the class average (mean) is 80% and you score 92%, the score is above the mean, so your z-score is positive.
Statistical Significance
Determined through hypothesis testing, which involves comparing observed data to what would be expected if there were no real effect/relationship. The null hypothesis states that there is no difference or relationship between two groups/variables, while the alternative hypothesis states that there is a difference/relationship. There is a chance that a rejected null hypothesis may be true. The amount of risk associated with rejecting the null hypothesis is the level of statistical significance. The maximum acceptable risk in social sciences is 5 chances in 100, denoted by p = .05 (p = probability).
Correlation
Aims to find a connection between two interval/ratio variables. The independent “x” variable is the (cause), and the dependent “y” variable is the (effect). Example: Consider the relationship between the size of the prison population (X) and the crime rate (Y). In the first case, the size of the prison population may affect the crime rate by deterring offenders. If a deterrent effect were present, the crime rate would go down when the size of the prison population increased. We would assume that X and Y are inversely (negatively) related. As the prison population (X) increases, the crime rate (Y) decreases.
The correlation coefficient is a number between -1 and 1 that measures the degree to which two variables are related. It indicates the strength and direction of a linear relationship between two variables. A linear relationship forms a pattern following one straight line. In a positive linear relationship, as the scores on the X variable increase, the scores on the Y variable also tend to increase (low to high). In a negative linear relationship, as the scores on the X variable increase, the scores on the Y variable tend to decrease (high to low). The strength of a relationship is the extent to which one value of Y is consistently paired with one and only one value of X.
Mixed Methods: Triangulation
A strategy that uses more than one theory or method to increase the validity of the findings. Different types of data are collected to measure and assess the same social problem and to increase our confidence in the inferences.
3 Types of Triangulation
- Investigator: To improve the credibility of the data and validity or trustworthiness of interpretations, this involves two or more researchers working on the same project and combining their expertise on the substantive topic and the method.
- Theoretical: Uses two or more theories to inform the research process.
- Methodological: Mixed methods. Two or more methods are used in the same research study.
Features of Mixed Methods
- Inclusion of a convincing rationale for why a mixed methods design is appropriate.
- Awareness of the research paradigm and philosophy of science for each of the methods.
- Demonstrated expertise in both methodological components of the mixed design.
- High multicultural awareness of the research team.
- Ethical vigilance that transcends both quantitative and qualitative components.
- Strong writing skills that incorporate qualitative components and objective precision in the quantitative component.
Advantages of Mixed Methods
- Words can be used to add meaning to numbers.
- Numbers can be used to add precision to words.
- Ability to answer a broader and more complete range of research questions by adopting more than one approach.
- The strengths of one method can overcome the biases and weaknesses in another method.
- Multiple types of data can provide stronger evidence to support a conclusion through corroboration of findings.
- Provide additional insight and understanding not possible with a single method.
- Potential to increase the generalizability of the findings.
Disadvantages of Mixed Methods
- Difficult for an individual researcher.
- Researcher must be knowledgeable in quantitative and qualitative methods as well as how to mix them appropriately.
- More expensive and time-consuming.
- Controversial with purists who argue that mixing paradigms/worldviews is philosophically inconsistent.
- Potential to decrease validity and reliability if quantitative and qualitative portions are not executed to their respective standards.
- Challenging to coordinate and manage data collection and analysis with complex mixed methods research designs.
Social Network Analysis
An approach to analysis/methodological techniques that help researchers describe/explore relationships that individuals/groups have. Social networks are types of relationships that can include face-to-face interactions, online/digital interactions, economic transactions, interactions with a criminal justice agency, geopolitical relations, and relations among nation-states. (Relational data measure the contacts/connections/attachments/ties that relate one unit to the next. Relational data are not properties of any particular unit (individual/group/city) but “relational systems” of units that are created by connecting pairs of interacting units (a technique to describe and examine relational data).
Sociograms
Graphs used to present social relationships. The basic units in graphs are called nodes, and nodes are connected by relations (entities, names).
Crime Mapping
Geographical mapping strategies used to visualize the location, distance, and patterns of crime, recidivism, and incarceration, and to create crime prevention strategies.
Geographic Information System (GIS)
A software tool (introduced in 1990) for displaying data on the Earth’s surface. It provides visual/statistical analysis of the nature of crime, allowing researchers to see relationships between crime and factors like poverty or school performance, and to visually communicate their analysis.