Amanda Smith
Discussion: The Logic of Inference: The Science of Uncertainty
All models are wrong. Some models are useful.
—George E. P. Box (1919–2013)
Statistician
Describing and explaining social phenomena is a complex task. Box’s quote speaks to the point that it is a near impossible undertaking to fully explain such systems—physical or social—using a set of models. Yet even though these models contain some error, the models nevertheless assist with illuminating how the world works and advancing social change.
The competent quantitative researcher understands the balance between making statements related to theoretical understanding of relationships and recognizing that our social systems are of such complexity that we will always have some error. The key, for the rigorous researcher, is recognizing and mitigating the error as much as possible.
As a graduate student and consumer of research, you must recognize the error that might be present within your research and the research of others.
To prepare for this Discussion:
· Search for and select a quantitative article that interests you and that has social change implications.
· As you read the article, reflect on George Box’s quote in the introduction for this Discussion.
· For additional support, review the Skill Builder: Independent and Dependent Variables, which you can find by navigating back to your Blackboard Course Home Page. From there, locate the Skill Builder link in the left navigation pane.
Discussion
Post a very brief description (1–3 sentences) of the article you found and address the following:
1. Describe how you think the research in the article is useful (e.g., what population is it helping? What problem is it solving?).
2. Using Y=f(X) +E notation, identify the independent and dependent variables.
3. How might the research models presented be wrong? What types of error might be present in the reported research?
Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style.
Lea
r
n
ing Objective:
Distinguish between independent and
dependent
variable
s
Words in orange represent glossary terms. You can locate the Glossary in Appendix 1.
Variables and Values
The ultimate goal of science is to identify and explain cause-and-effect relationships among events in the real world. For example, a researcher may want to understand how a person can grow thicker hair. This researcher may think that using high-quality shampoo, specifically Ultra Shampoo, will result in thicker hair. How should the researcher structure questions about whether this specific shampoo brand promotes thick and luxurious hair?
A
quantitative
researcher’s approach to this problem begins by using variables. A variable is a mathematical representation of the real-world entity being measured. For example, the researcher could decide that “use” or “non-use” of Ultra Shampoo is one variable. A measure of hair quality, as judged by a professional hairstylist, could be a second variable.
Variables are sometimes called attributes, traits, or constructs and can actually take on two or more
value
s. The value of a variable is defined as a single observation for the variable. Going back to the example, if a person uses Ultra Shampoo, the researcher could code “Yes” as a value for the use of the Ultra Shampoo variable and “No” for its non-use. Similarly, a “10,” corresponding to perfect hair, could be a value for a single person on the hair quality variable.
The image below shows how variables and values appear in data sets. Note that a person’s name is used as a variable so that the name will identify the values for the study participant on the other two variables.
Cause and Effect Relationships
Again, the ultimate goal of science is to identify and explain cause and effect relationships among events in the real world. Questions about cause-and-effect are everywhere. For example: Does smoking cause cancer? Does daily exercise minimize anxiety? Does transformational leadership result in job satisfaction? Essential to determining cause-and-effect relationships is recognizing that some variables are independent and some are dependent.
· bullet
The
independent variable
is defined as the variable that is studied to see if it causes a change in the dependent variable. Put another way, the experimental manipulations (such as
control group
s) a researcher uses are reflected in the independent variable.
· bullet
The dependent variable is defined as a measure of the outcome: that is, the dependent variable allows the researcher to determine whether the independent variable has an effect.
For example, in the hypothetical study of how a brand of shampoo affects hair quality, the researcher could randomly assign some people to use Ultra Shampoo and others to use a competing brand of shampoo. In this situation, the type of shampoo would be the independent variable and hair quality would be the dependent variable.
Topic 4 of 4
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Term |
Meaning |
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+∞ |
Positive infinity. |
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-.564 |
Observed value of the test statistic. |
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-∞ |
Negative infinity. |
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.004 |
p-value |
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.576 |
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2-tailed |
The alternative hypothesis states simply that there is a difference between the mean s but does not specify the direction of the difference. |
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61 |
61 is the degrees of freedom (df) calculated by n-2 (63-2) |
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alpha |
The probability of a type I error. |
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box-plot |
A graph that displays key element s of distribution. |
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categorical variables |
Variables that have a limited number of possible values; participants in the study get placed into one of a small number of categories for the variable. |
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central limit theorem |
regardless of the distribution of the population , if the sample size is relatively large (a rule of thumb is n > 30), the sampling distribution of sample means is close to normal. |
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cohen’s d |
A measure of effect size. |
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confidence interval s |
A range of values used to specify the likelihood that the population parameter is contained within a specified range. |
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continuous variable |
A continuous variable is one based on an interval or ratio level of measurement. Between any two values for the variable, there is another possible value. |
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continuous variables |
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| control group |
The collection of participants in the condition of an experiment who do not receive the treatment. A group receiving an actual treatment can then be compared to the control group. |
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| dependent variable |
A measure of the outcome that allows us to determine whether the independent variable has an effect. |
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discrete |
A variable based on an ordinal , interval, or ratio levels of measurement and has a countable, not infinite, set of possible values. |
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distribution of a population |
The distribution of all values for all elements of the population. |
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distribution of a sample |
The distribution of actual observations based on the data that you collect. |
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distribution of the sample |
Sample distribution (also called distribution of the sample) –for a variable, the distribution of values for the elements of the population that are actually observed. (note that Sample distribution is different from Sampling distribution). |
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| element |
an entity in the population that may be selected for the sample and then observed. |
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factor |
The alternative hypothesis stated simply that there was a difference between the means, and does specify the direction of the difference. |
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frequency distribution |
A table or graph that shows the values of a variable and the number (count) of observations associated with each value |
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general rule |
Although different sources give slightly different information about assessing the strength of a correlation coefficient, we can use the following as a general rule for interpreting the correlation coefficient:.8 to 1: very strong.6 to .8: strong.4 to .6: mode rate.2 to .4: weak0 to .2: very weak to no relationship |
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| independent variable |
The variable that is studied to see if it causes a change in a dependent variable. |
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| interval |
The level of measurement that addresses differences, or intervals, between entities. |
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interval estimates |
A range of values that is likely to contain the population parameter. |
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levels of confidence |
The probability that the population parameter is contained within a specified range of values. Usually, the level of confidence is 0.95 or 95%. |
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| levels of measurement |
Also called scale of measurement, describes the amount and type of information ( nominal , ordinal, interval, and ratio) that is conveyed by the numbers or words assigned to real-world objects during the measurement process. |
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levene’s test |
Tests the null hypothesis that the two populations show equal variance . |
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margin of error |
The amount of estimated error in the point estimate of a population parameter determined by the level of confidence and the sampling distribution for the sample statistic. In estimating the population means, the margin of error equals a critical value for statistic times the standard error of the mean, e.g., Zα2*σn. |
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| mean |
The average of the scores for a variable. |
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median |
An appropriate measure of central tendency when a measurement is at the ordinal, interval, or ratio level. |
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| mode |
The most frequently occurring value in the data set. |
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| n |
n = sample size |
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n1 |
n1 = the number of participants in sample 1 |
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n2 |
n2 = the number of participants in sample 2 |
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negative skew |
This refers to the tail of the distribution appearing longer on the left-hand side of the distribution. |
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| nominal |
The lowest level of measurement, which addresses naming—identifying or categorizing objects using a name. |
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one-tailed |
The alternative hypothesis is directional and states that one mean is greater than the other. |
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| ordinal |
The level of measurement above nominal that addresses ordering real-world entities. |
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outliers |
Observation points that are distant from other observations. |
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p <.01 |
This indicates that the p-value (.000) is less than .01 and that the correlation test is statistically significant . |
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The probability of obtaining a result equal to or “more extreme” than what was actually observed, when the null hypothesis is true. |
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pictogram |
A graphic character used in picture writing. |
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| point estimate |
An estimate of the unknown parameter of interest using a single value. |
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| population |
The set of all possible elements (entities and observations) to which the researcher wishes to generalize. |
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population distribution |
for a variable, the distribution of all values for all elements of the population. |
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positive skew |
This refers to the tail of the distribution appearing longer on the right side of the distribution. |
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qualitative |
A variable based on nominal measurement. |
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| quantitative |
A variable with an ordinal, interval or ratio level of measurement. |
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| r |
r is the symbol indicating a Pearson’s correlation coefficient |
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r-squared |
The proportion of variability in the dependent variable that is accounted for by your model. |
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random assignment |
Random assignment is placing experimental units in treatment conditions or control conditions by use of a random process. |
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random sampling |
The selection of experimental units so that each element in the population has the same chance of being selected for the sample. |
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random variable |
A variable whose value is determined by a random process such as being selected in a survey or being observed in an experiment. |
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| ratio |
The level of measurement that addresses proportion, or ratios between entities. |
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| ratio level |
The level of measurement that addresses proportion, or ratios, between entities. |
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relative frequency distribution |
A table or graph that shows the values of a variable and the proportion of observations associated with each value using decimal fractions or percentages. |
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research design |
The overall plan for how a researcher will collect data. |
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| sample |
A subset of all possible observations. |
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| sampling distribution |
The distribution of a sample statistic. |
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sampling distribution of the sample mean |
The distribution of values for the sample mean for all possible random samples of size n. |
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sampling error |
The absolute value of a statistic minus the parameter being estimated. |
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simple random sampling |
Each unit in the population has an equal chance of being selected into the sample. |
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statistical analyses |
The use of probabilistic models to analyze data. |
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statistical inferences |
the process of using sample information to make statements about population parameters. |
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statistical power |
The probability of rejecting a null hypothesis if the null is false (i.e., the alternative is true). |
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| statistically significant |
Statistical significance means a null hypothesis has been rejected. |
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|
t-test for two independent groups |
A statistical test used to examine whether two independent groups have different means on a dependent variable. This test is also sometimes referred to as an independent samples t-test. |
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two-tailed |
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type i error |
Rejecting the null hypothesis if the null is actually true. |
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type ii error |
Incorrectly retaining a false null hypothesis (a “false negative”). |
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unit of analysis |
The real-world entity that is observed and for which data are recorded and used in statistical analysis. |
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| value |
A single observation defined for a variable. |
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| variable |
The mathematical representation of the real-world entity being measured. |
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| variance |
Variance is a measure of variability in a set of observations based on the approximate average of squared deviations from the mean. |
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visual displays of data |
Help researchers communicate the distribution and other key information (the story they are telling with their data) both effectively and efficiently. |
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µ1 |
mean for population 1 |
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µ2 |
mean for population 2 |
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β |
β is the symbol researchers use when they report a standardized regression coefficient. |
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μ not primed |
This indicates the population means for the “not primed” condition. |
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μ not primed – μ primed >0 |
The alternative hypothesis specifies that the “not primed” condition will score higher than the “primed” condition. |
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μ primed |
This indicates the population means for the “primed” condition. |