Test 3 Descriptive (simple and summary) and inferential statistics

Descriptive statistics

numbers or numerical representations (ex: graphs & tables) that describe basic characteristics of your sample

Simple descriptive statistics

total counts (or frequencies) OR total proportions (or percentages) of case types in your sample (ex: total # / % male/females)

Summary descriptive statistics

provide straightforward, slightly more sophisticated info on sample characteristics; has 3 types

What are the three types of summary descriptive statistics?

Central tendency (mean, median, and mode), skewness, and variability

Inferential statistics

numbers or numerical representations that summarize how likely and how much the associations between variables in sample exist in population

Descriptive statistics appropriate for what type of research?

Both always provided by deductive, but usually simple descriptive statistics are used for inductive

Inferential statistics appropriate for what type of research?

Only provided for deductive research studies bc it requires random/probability sampling

Inductive research

data → empirical patterns → theory; quantitative; non-probability sampling

Deductive research

theory → hypothesis → data; qualitative; probability sampling

Definition of Variability

how spread or clustered the data values are

Types of variability

range, interquartile range, variance, standard deviation (SD), and index for qualitative variation (IQV)

Range of Variability

highest minus lowest value for particular variable; weakness=sensitive to outliers risking uninformative static

Interquartile range of Variability

range for middle 50% of cases, cutting lowest and highest quartiles leaving out potential outliers

Variance of Variability

average distance of each case from center of the data distribution; if really spread out, average distance of all from middle have a large variance and if not spread, average distance from middle is small variance

Standard deviation (SD) of Variability

square root of variance

Index for qualitative variation (IQV) of Variability

statistic for calculating variability in a nominal variable (categories like yes/no) ranging from 0-1

What does 0 to 1 mean for the Index for qualitative variation (IQV) of Variability?

0=no variability whatsoever, every case is same response and 1=maximum variability with cases uniformly distributed across all responses

When to use variability:

Range, iqr, and sd for interval-ratio variables BUT iqr typically for ordinal variable

Definition of Central Tendency

the middle on data and where it is centered

Types of Central Tendency

mode (most frequent value), median (where data splits in half, put in order), and mean (average of data)

When to use central tendency?

Mode best to describe nominal variables, median good for interval/ratio values with big outliers, and mean ONLY for interval/ratio values

Definition of Skewness

shows whether more cases in a sample are more concentrated on one side of the variable option compared to the other; shows asymmetry of data distribution

Types of Skewness

positive/right skew, negative/left skew, normal distribution, or uniform distribution

Positive/right skew

tail on the right side, from peak order: mode, median, and mean

Negative/left skew

tail on the left side, following up to peak order: mean, median, mode

Normal/symmetrical distribution

bell shape; median, median, and mode are at the peak

Uniform distribution

equal distribution and frequency for all variables

When to use skewness?

Positive for income data, negative for age at retirement, symmetrical for height in a population

Levels of measurement

Nominal/ordinal/interval/ratio

Nominal

Label or categorize data without any order or ranking, no math

Ordinal

Order or ranking, represent nothing more than the order of categories; not say how greater one category is than other, how much on scale

Interval

Measure data with equal intervals between values, but there is no true zero point addition and subtraction (i.e temp)

Ratio

Measure data with equal intervals between values with true zero point, can add, subtract, multiply, and divide (i.e weight, income, age)

Types of graphs

bar charts/histograms, frequency polygons

What variables are bar charts/histograms used for?

Ordinal, ration & interval variables; A bar chart is used to compare discrete categories, while a histogram displays the distribution of continuous data

What variables are frequency polygons used for?

Ordinal, ration, interval, but best for ratio/interval variables if big range

Types of tables

descriptive statistics table, correlation tables, group statistics table, independent samples test table, and frequency distribution table

What variables are descriptive summary statistics tables used for?

Interval and ratio variables

What variables are correlation tables used for?

Interval and ratio variables (c)

What variables are frequency distribution tables used for? HINT: IV

Nominal, ordinal, and discrete variables

Statistical significance

likelihood that a result or relationship in data is not due to random chance, sampling error

Standard of statistical significance

p value is p<0.5 (less than 0.5) which signifies less than 5% likelihood that the association between the IV and DV is due to sampling error alone and can reject the null hypothesis (effect being studied does not exist).

How to describe statistical significance:

With a t-test result of p<.076, there is more than 5% probability that a relationship as strong as the one observed in the sample is due to random error alone. We cannot claim statistically significant results, and we fail to reject the null hypothesis

Experiments

quantitative method often used for deductive inquiry; theory→hypothesis→data

Essential characteristics/requirements of experiments

1 or more manipulated IV/”treatments”, 1 or more measured DVs, 2+ respondent groups randomly assigned to different IV conditions but treated equally

What is the logic of experimentation?

Association (assess whether IV and DV vary jointly), direction of influence (guarantee exposure of IV occurs before DV), and non-spuriousness (minimize risk of fake relationship through random assignment and controlled environments)

Reasons to use factorial design

to provide evidence of the impact of each factor as well as the joint effect of the factors

Characteristics of factorial design

An experiment in which two or more variables (factors) are manipulated.

Reasons to use field experiments

To observe genuine behaviors in natural environments and test effectiveness of interventions in real-life contexts

Characteristics of field experiments

manipulation of independent variable, random assignment, less control of extraneous variables

Reasons to use survey experiments

To assess how different framings or information affect attitudes and opinions and to conduct experiments efficiently with broad populations

Characteristics of survey experiments

combines experimental manipulation with survey, allows for causal inference

Reasons to use audit studies

to examine real-world settings of racial and other forms of discrimination by sending matched pairs of individuals to apply for jobs, purchase a car, rent an apartment, and so on

Characteristics of audit studies

highly controlled to isolate variable of interest, measures actual behaviors, a type of field experiment

Correct order of steps in experimental research

Design experiment, rehearse (practice experiment w/ participants), recruit participants, introduce and obtain consent for experiment, random assignment, conduct pre-test, implement treatment, conduct manipulation check, measure DV/post-test, debrief

Reasons for pre-check/post-check design

DV measured both before AND after IV exposure to obtain baselines for participants and experimental vs. control groups

Manipulation check

making sure the IV was actually perceived as intended and can occur EITHER immediately after a “treatment” or end of study

Informed consent

honestly explain possible harms and benefits without giving away cover story, remind that participation is voluntary, and exit is is always an option

Debriefing

occurs after conclusion of data collection to inform of deception and ask understanding of directions, belief in cover story, why the response to stimulus, any psychological discomfort, and request not sharing information to others

Cover story

believable, sensical introduction to study that obtains cooperation while disguising research hypothesis

Reactive measurement effects

effect in which participants’ awareness of being studied produces changes in how they ordinarily would respond, only affects DV

Types of measurement effects

contamination, hawthorne effect, placebo effect, self-fulfilling prophecy

Contamination RME

study participants become aware of group assignment

How to mitigate risk of contamination RME

limited duration of experiment, request for nondisclosure

Hawthorne effect RME

participants alter behavior under observation

How to mitigate risk of Hawthorne effect RME

prolonged observation, covert observation, “single-blind” experiment, and effective cover story

Placebo effect RME

participants “improve” in DV due to receiving treatment/attn

How to mitigate risk of placebo effect RME

control group receives a fake or neutral treatment that looks or feels like the real treatment but has no active effect

Self-fulfilling prophecy RME

researchers’ reactions give away treatment conditions

How to mitigate risk of self-fulfilling prophecy

“double-blind” experiment (both researcher and participant don’t know treatment during experiment)"

Methods to improve experiments' external validity

replication and sacrifice internal validity

External validity

extent to which experimental findings may be generalized to other settings, measurements, populations, and time periods

Replication to improve external validity

repeat the experiment with different kinds of samples, under different settings, at different times

Sacrifice internal validity to improve external validity

Conduct alternative experiments or quasi-experiments that occur outside of laboratory contexts and that the researcher cannot strictly control

Participants involved in Correl et al “Getting a Job Is there a Motherhood” study

undergraduates that evaluated the resume and job application in laboratory experiment and real employers in audit study

Dependent variables measured in Correl et al “Getting a Job Is there a Motherhood” lab study

ability standards for recommended salary low for mothers, estimation of likelihood of promotion, judge whether applicants if hired should be recommended for management-training course, or if hired or not at all.

Dependent variables measured in Correl et al “Getting a Job Is there a Motherhood” audit study

callback rates

How they achieved control in lab study

matched resume only parental, race, and gender status diff, random assignment, gendered names and race, and blind about hypothesis

How they achieved control in audit study

same gender, equally qualified, same sex, but different parental status (one is a parent and one not)