Quantification & Measurement Flashcards
What is the process of psychological research?
1. Collect observations on existing theory
2. Develop a testable hypothesis
3. Conduct study to test the hypothesis and eliminate alternative hypotheses
4. Analyze data and interpret results
5. Apply results to existing theory
What are the 3 ways in which math and statistics aid scientific study?
Quantification - using numbers to represent quantities of concepts
- *Theoretical Modelling** - using math/stats to model and predict the behavior of natural systems
- *Weighing Evidence** - decide the relevance of different trials and how they reflect reality
What is a variable?
A characteristic that can vary or take on values.
What is a value?
A number representing possible states of the variable.
What is a score?
A specific value for a subject.
What is critical to systematic measurement?
A well-defined or quantitative system of measurement; system must be standardized.
What is a quantitative statement?
Any statement where variables are assumed to be able to be numerically quantified.
What are categorical variables?
Variables that have no numerical significance; they are not evaluated against each other, ordered, or ranked in any way. Each answer is not numerically meaningful.
What are continuous variables?
Variables that have numerical significance. They can be ordered, ranked, and quantified against one another; they “vary in a graded way.”
What are continuous variables grouped into?
- Ordinal - designates an ordering; quasi-ranking. Intervals are not equal.
- Interval - designates an equal-interval ordering.
- Ratio - designates an equal-interval ordering with a true zero point (i.e., the zero implies an absence of the thing being measured)
What is a frequency table?
A table showing how often each score occurs.
What is a grouped frequency table?
A table where the intervals are made larger to accommodate for more scores, or 0 frequencies of scores.
What is a frequency polygon?
A visual representation (i.e. line graph) of a frequency table of scores.
What do pie charts often represent?
Nominal data, like age ranges, gender, and other demographics.
What do bar charts often represent?
The frequency of scores for nominal data.
What do the visual aides for data (e.g. histograms, bar charts, frequency tables, frequency polygons, etc.) represent?
Frequency distributions.
What are frequency distributions?
The way score frequencies are distributed with respect to the values of the variable.
What happens in a unimodal distribution?
One score occurs more or significantly more than other scores in the distribution.
What happens in a bimodal distribution?
Two modes (i.e. most frequently occurring score) exist.
What happens in a multimodal distribution?
More than two modes (i.e. most frequently occurring score) exist.
What are rectangular or uniform distributions?
All values are observed equally often; the distribution is literally symmetrical.
What does a normal distribution resemble?
A bell; called a bell curve.
What are skewed distributions?
Scores cluster to the right or the left of the distribution.
What are the 3 measures of central tendency?
Mean - The “balancing point” of a set of scores; the average.
Median - the value at which 1/2 of the ordered scores fall above and 1/2 of the scores fall below
Mode - most frequently occurring score
Why is the mean considered a balancing point?
The sum of all the mean deviations is 0.00.
Where do scores fall when the distribution is normal?
Mode = Median = Mean
Where do scores fall when the distribution is negatively skewed?
Mode > Median > Mean
Where do scores fall when the distribution is positively skewed?
Mode < Median < Mean
Why is the mean the most commonly used measure of central tendency?
1. It uses all the information in the scores.
2. It can be algebraically manipulated w/ ease.
What is spread/dispersion?
The degree to which scores are clumped around the mean; how far, on average, an individual score is from the mean.
What are the 3 measures of spread?
1. Variance - average of squared differences; tells nothing about how the scores differ
2. Standard Deviation - how far, on average, scores are from the mean.
3. Average Absolute Deviation - how far the typical score is from the mean.
What do deviation scores sum to?
0.
What is variance?
The average squared deviation score; the average of the squared differences from the mean.
What is standard deviation?
The square root of the average squared deviation score.
What do standard scores represent relative to?
- The mean of the group; how far an individual score is from the mean
- The variability of the scores within the group
What are the 3 properties of a set of z-scores, or standardized scores?
1. The mean of a set of z-scores is always zero
2. Standard deviation of a set of standardized scores is always 1
3. The distribution of a set of standardized scores has the same shape as the unstandardized scores
What is different about a set of standardized vs. unstandardized scores regarding shape?
The scaling or metric is different, even if the shape is still the same.
What are the two advantages of using z-scores?
1. To find centile scores: the proportion of people with scores less than or equal to a particular score. Help define where an individual score falls w/ respect to other scores.
2. Standard scores provides a way to standardize or equate different metrics. They can be evaluated relative to one another, even if they measure different concepts.
Why can z-scores be used to represent/equate different metrics?
Any score comes from a distribution w/ the same mean (i.e. 0) and standard deviation (i.e. 1). Evaluates both scores relative to standard deviation distribution as opposed to frequency distribution of individual scores.
What are two disadvantages of using z-scores?
- Because a person’s score is expressed relative to the group(X - M), the same person can have different z-scores when assessed in different samples. Score depends on the other scores in any unique sample.
- If the individual score is meaningful or of psychological interest, it will be obscured by transforming it to a relative metric.
In bivariate association, how do we define high vs. low scores?
Study deviations from the mean (X - Mx) and (Y - My).
What is a limitation in bivariate association of only counting the matching scores individually?
There are clearly different magnitudes of association that would count as perfect matches. Association is not well-defined or standardized.
What is covariance?
The correspondence between the average deviation scores on two variables—the extent to which those deviation scores [of each of the two variables] vary together.
What is positive covarying/covariance?
Average product is positive. Scores which are high on one variable tend to be high on the other.
What is negative covarying/covariance?
Average product is negative. Scores which are low on one variable tend to be low on the other.
What is no covariance?
Average product is 0. Scores are just as likely to be high or low on either variable.
What is a regression line?
The estimated linear relationship between the two variables; used in modelling.
What is a limitation of covariance?
The size of the covariance depends on the variability of the variables.
What does the limitation of covariance make difficult to measure?
The magnitude of the covariance b/w variables; how strong the relationship b/w the variables is.
What does a variable covary with most strongly out of all possible variables in a sample?
Itself. This is another way to define variance.
What do we want to evaluate the covariance relative to?
A value of 1 or -1.
What does correlation do?
Standardize covariance of multiple variables relative to the product of the standard deviations for those variables; the product of the SDs is the maximum amount of variability possible b/w the metrics.
What can correlation also be understood as?
The average product of z-scores. This is identical to standardizing covariance.
What can the value of r (correlation) range b/w?
1 and -1.
What does it mean when r = 0?
There is no correlation.
What does it mean when r = 1 or r = -1?
There is a perfect positive or negative correlation within the variance of the sample/population.
What does the size of the correlation correspond to?
The strength of the relationship b/w variables.
What are the advantages of the correlation coefficient?
1. Easily quantify the association b/w variables
2. Uses z-scores
3. Variances are standardized and equal to 1
4. Foundation for many stat applications
