291 - Set 1
median (mdn)
-the *middle score* in a distribution; half the scores are above it and half are below it (just put in order and pick the middle value - if even, median is the average of two middle scores) -not guaranteed 50/50 split (if even) -only score guaranteed to be in the middle (50th percentile point) -may not be in the data set (if even) -has to be at least ordinal (because need it in order) -*not affected by extreme scores* - good to report income, etc.
mean
-the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores -repeated most often/represents most *-only measure of central tendency that uses all the data in the set* -needs equal spacing (at least interval) -often not part of the distribution set -affected by every score in data set (*highly sensitive to extreme scores*) -*balance point of distribution* (sum of deviation about the mean = zero) (deviation: difference between one score and the average) - see formula in notes -mean is the one value that is closest to all values simultaneously (*least total error*)
mode (mo)
-the most frequently occurring score(s) in a distribution -possible to have more than one 0 modes (uniform distribution or non-modal), 1 mode (uni-mode), 2 modes (bi-mode), 3+ (multi-mode) -can even use nominal data *-most sensitive to sampling variability* -assuming it exists, reps single largest group in data set -may not rep data set as a whole -change the location of one value, can change the mode -interpret with caution
State three commonly used research methods?
experimental, quasi-experimental and correlational
ratio scale of measurement
measurements that have a true zero and are distributed in equal units
interval scale of measurement
measurements that have no true zero and are distributed in equal units
which type of central tendency is always located at the center of the distribution
mode
nominal scale of measurement
represent something or someone, and are often data that have been coded
scales of measurement
rules for how the properties of numbers can change with different uses
descriptive statistics
statistics that describe the characteristics of some group, event, behavior, etc. procedures used to summarize, organize, and make sense of a set of scores called data
control group
the group that does not receive the experimental treatment
weighted mean
the mean obtained by assigning each observation a weight that reflects its importance
independent variable
the variable that is manipulated in an experiment. This variable remains unchanged (or "independent") between conditions being observed in an experiment. It is the "presumed cause." The specific conditions of an IV are referred to as the levels of the independent variable.
dependent variable
the variable that is measured in each group of a study, and it is believed to change in the presence of the independent variable. It is the "presumed effect."
quantitative variable
varies by amount. This variable is measured numerically and is often collected by measuring or counting.
qualitative variable
varies by class. This variable is often represented as a label and describes nonnumeric aspects of phenomena.
A researcher tests whether citizens of differing political affiliations (Republican, Democrat) will show differences in attitudes toward morality. Is this an experiment, a quasi-experiment, or a correlational method?
Quasi-experiment
the 3 measures of variability
Range - highest score minus lowest score (real range - same plus 1 - all values) *-only tells you about extreme scores (least useful)* Standard Deviation - average amount of scores differ from the mean Variance - Standard Deviation squared See symbols for these in notes
experiment
a study in which researchers satisfy three requirements to ensure enough control to allow them to draw cause-and-effect conclusions. *Manipulation (of variables that operate in an experiment) *Randomization (of assigning participants to conditions) *Comparison/control (a control group)
quasi-experimental method
a study that (1) includes a quasi-independent variable and/or (2) lacks a comparison/control group.
Independent variable or quasi-independent? a.) Environment of research setting b.) Years of education c.) Type of feedback (positive/negative)
a.) Independent b.) Quasi-independent c.) Independent (if feedback was coming from researcher)
Independent variable or quasi-independent? a.) Martial Status b.) Political affiliation c.) Time of delay prior to recall
a.) Quasi-independent b.) Quasi-independent c.) Independent (could manipulate in a way that could end either way)
A researcher tests whether cocaine increases impulsive behavior in a sample of cocaine-dependent and cocaine-inexperienced mice. a.) Identify the independent variable b.) Identify the dependent variable
a.) cocaine use b.) impulsive behavior
correlational method
can determine whether a relationship exists between variables, but it lacks the controls needed to demonstrate cause and effect.
Which variable is measured in each group? Which variable is manipulated?
dependent independent
sampling variability
*-the natural tendency of randomly drawn samples to differ* -either the difference between a sample and the population it was drawn from (ie - our class GPA vs GPA from school) -or the difference between multiple samples drawn from the same population (ie - GPA from 3 different stats classes) *-need to know sample is not going to be 100% match to population*
rules of interval notation
-all intervals must be same width - lowest interval must contain lowest score - highest interval must contain highest score -when calculating - range divided by total values (round that number to nearest odd number (start with multiple of that calculated interval width) (ie - 19/4 = 4.75 - width is 5 and intervals should be in multiples of 5)
Why would a researcher summarize data with a bar graph instead of a histogram?
A bar chart would be used for summarizing discrete or categorical data (gaps between the bars signify breaks between the categories or numbers). A histogram would be used for continuous data (no gaps).
frequency distribution
A summary chart, showing how frequently each of the various scores in a set of data occurs
Distinguish between descriptive and inferential statistics.
DS - summarizes characteristics of a population IS - generalizes characteristics of a population from a sample
A researcher measures the relationship between annual income and life satisfaction. Is this an experiment, a quasi-experiment, or a correlational method?
Correlational method
A researcher measures the height and income of participants and finds that taller men tend to earn greater incomes than do shorter men. What type of research method did the research use?
Correlational method - since the height and income of participants were calculated and compared to see how they may be related to each other.
What are the two types of variables that can be quantitative?
Discrete and continuous
Is a pie chart typically used to summarize continuous or discrete/categorical data?
Discrete/Categorical Data (i.e. - gender, yes, no, etc. the pie char is a circle in which parts are divided to show proportion of a whole).
A researcher tests whether the dosage level of some drug (low, high) causes significant differences in health. Is this an experiment, a quasi-experiment, or a correlational method?
Experiment
A researcher demonstrates that eating breakfast in the morning *causes* increased alertness throughout the day. What research design did the researcher use?
Experimental research design because it claims to have demonstrated a cause.
True or false: Qualitative variables can be continuous or discrete.
False. Qualitative variables can only be discrete
What is the key difference between grouped and ungrouped data?
Grouped data are distributed into intervals. Ungrouped data are not (kept as individual scores).
Percentile rank
How much of the distribution is below you (you beat)
Rank the scales of measurement in order from least informative to most informative.
Nominal (label, category, name) Ordinal (magnitude) Interval (equal spacing) Ratio (true zero point)
Type of Variable - Best measure of central tendency
Nominal - Mode Ordinal - Median Interval/Ratio (not skewed) - Mean Interval/Ratio (skewed) - Median
Midpoint
Plot if interval width is odd Will always be a whole number
Percentile point
Score you need for raw percentile
(1) name the variable being measured, (2) state whether the variable is continuous or discrete, and (3) state whether the variable is quantitative or qualitative. A researcher asks children to choose which type of cereal they prefer (one with a toy inside or one without). He records the choice of cereal for each child.
The choice of cereal (the variable) is discrete and qualitative.
(1) name the variable being measured, (2) state whether the variable is continuous or discrete, and (3) state whether the variable is quantitative or qualitative. A researcher records the month of birth among patients with schizophrenia.
The month of birth (the variable) is discrete and qualitative.
(1) name the variable being measured, (2) state whether the variable is continuous or discrete, and (3) state whether the variable is quantitative or qualitative. A professor records the number of students absent during a final exam.
The number of absent students (the variable) is discrete and quantitative.
(1) name the variable being measured, (2) state whether the variable is continuous or discrete, and (3) state whether the variable is quantitative or qualitative. A therapist measures the time (in hours) that clients continue a recommended program of counseling.
The time in hours (the variable) is continuous and quantitative.
The upper boundary of one interval and the lower boundary of another do not overlap in simple frequency distribution. Why?
To ensure that a single score cannot be counted in more than one interval.
An experiment is the only method that can demonstrate cause-and-effect relationships between variables. True or false?
True
parameters; statistics
__________ describe(s) characteristics in a population, whereas _____________ describe(s) characteristics in a sample.
quasi-independent variable
a preexisting variable that is often a characteristic inherent to an individual, which differentiates the groups or conditions being compared in a research study. Because the levels of the variable are preexisting, it is not possible to randomly assign participants to groups. (sex, gender, etc)
Continuous or discrete variable? a) time in seconds to memorize list of words b.) number of students in a statistic class c.) weight in pounds of newborn infants d.) SAT scores among college students
a.) continuous b.) discrete c.) continuous d.) discrete
To determine whether a new sleeping pill was effective adult insomniacs received a pill (either real or fake/placebo) and their sleeping times were subsequently measured (in minutes) during an overnight observation period. a.) Identify the dependent variable b.) Identify the independent variable
a.) effectiveness of sleeping pill (sleeping time, in minutes). b.) sleeping pill
Is it necessary to compute the real range to construct a frequency distribution for a.) ungrouped data? b.) grouped data? ((((SEE IF B IS TRUE))))
a.) for ungrouped data, the dependent variable is qualitative or the number of different scores is small. For this type of data, intervals are not created. So, no it is not necessary. b.) for grouped data, a set of of scores is distributed into intervals where the frequency of each score can fall into any given interval. To construct a frequency distribution for grouped data, the real range is obtained where the real range is one more than the difference of the largest and smallest value in the data set. NOT SURE ABOUT THE FOLLOWING...So, not necessary to compute the observed range to construct a frequency distribution for grouped data.
Study measures qualitative or quantitive variable? a.) open-ended questions asking how they feel when they are in love b.) blood pressure taken during task that meant to induce stress. c.) drug addiction study - injects rats with attention inducing drug that measures rate of lever-pressing d.) witness of crimes give description of suspect
a.) qualitative b.) quantitative c.) quantitative d.) qualitative
the median is an appropriate measure for describing what types of data?
data that are skewed and ordinal data
inferential statistics
make predictions / draw inferences about the larger group generalize from samples to populations
central tendency
mean, median, mode
continuous variable
measured along a continuum at any place beyond the decimal point. A continuous variable can thus be measured in fractional units.
continuous variable
measured along a continuum at any place beyond the decimal point. can thus be measured in fractional units.
ordinal scale of measurement
measurements that convey order or rank alone
A researcher measures four variables: age (in days), speed (in seconds), height (in inches), and movie ratings (from 1 to 4 stars). Which of these variables is not an example of a variable measured on a ratio scale?
movie ratings (from 1 to 4 stars)
the mode is an appropriate measure for describing what types of data?
nominal, freq occurring scores usually given with mean or median
the four scales of measurement
nominal, ordinal, interval, and ratio
the mean is an appropriate measure for describing what types of data?
normally distributed, interval and ratio scale
In 2010, Fortune magazine ranked Apple as the most admired company in the world. This ranking is on a(n) ____________ scale of measurement.
ordinal
true zero (absolute zero)
when the value 0 truly indicates nothing on a scale of measurement. Interval scales (like degrees) do not have a true zero.