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Often one either isn’t able or won’t want to describe a full set of observations completely
Lack means (e.g., time, opportunity, space,...)
Target of message lacks capacity;
May not be needed in many instances
Often sufficient to summarize large sets of observations.
Ultimate summarization is to reduce a large set of observations to a single value--a (descriptive) [central tendency] statistic |
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Central Tendency
Variability
Other distributional features
Proportions
Graphic descriptions |
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| measures of central tendencies |
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=(X1,1 + X1,2 + ... + X500,7)/3500
That is also the point that would put the board in balance, like a see-saw.
It’s the perfect “balancing point” for all the scores. |
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Are easy to compute
Lend themselves to useful inferences
(because means have certain useful statistical properties)
Are sensitive to every score, especially to extreme scores
Generally, changing a score will change it
Adding or subtracting a score will affect it
Adding or subtracting an extreme score can powerfully affect it
Easy to see on the “see-saw”; adding one more person further out makes you move the fulcrum point toward him/her
Can (falsely) give an illusion of great precision |
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Is the “middlemost” score,
Divides the top and bottom half of the observations
-fairly sensitive to extreme scores.
Is the 50th percentile |
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| when will the mean= the median |
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| Anytime the distribution is symmetric |
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| " distribution of scores" |
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| A1: a graph or plot that summarizes the scores |
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| distribution is symmetric |
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that there is some point that divides all the scores up into “mirror images” of one another
for every scores above that point, there is it’s mirror image the same distance below
if you “folded the distribution over” at that point, the one side would fit right on top of the other side |
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| Is the “most popular” score, the one that occurs the most |
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| range, interquartile range, variance, standard deviation |
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difference between highest and lowest score
can be too sensitive to a single extreme score |
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difference between the 75th and 25th precentiles
less sensitive to most extreme scores |
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| mean of squared deviation from the mean = |
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square root of variance = σ
variances and standard deviations are very useful for doing statistics and for conveying lots of information
e.g., especially if observations are distributed “normally” (in a normal distribution) |
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| summarizes the degree of asymmetry |
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| means that the distribution is symmetric |
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| means that the distribution has a “tail” in the positive direction |
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| means that the distribution has a “tail” in the negative direction |
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Use of a Mode as a central tendency statistic assumes that the most common response is the most descriptive of the whole distribution
likely to be true if there is a single Mode
but distributions can have more than one “peak” |
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1) when they “go together”
e.g., as one goes up, the other goes up--positive relationship
e.g., as one goes up, the other goes down--negative relationship
2)whenever (as) different values on variable A are observed, different values on variable B are observed
3)knowledge of a person's value on variable A improves our ability to predict that person's value on variable B (relative to how well we could have predicted without knowing A) |
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| absence or lack of relationship means |
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1)as one goes up (or down), the other stays the same
2)as different values on Variable A are observed, the same values on Variable B are observed (that is, Variable B remains constant)
3)knowing A gives us no improved ability to predict B (over not knowing A) |
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| In a 2x2 table, in order for there to be a relationship, all you need to do is show either |
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Definition
that the row relative frequencies differ within either column
or, that the column relative frequencies differ within either row |
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___ ____ between A and B is one where knowing one’s standing on Variable A tells you exactly what one’s standing on Variable B is
if the relationship between A and B were held to be “the rule”, there are no “exceptions to the rule” for ____ ____
Synonyms: deterministic relationship |
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| not enough info to establish a relationship |
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| singe cell error-only know one persons story |
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| single cell error-the satisfied customer "this treatment really works" |
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| reasoning from ones own experience |
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| single cell error "if you work hard you'll be successful like me. i worked hard and im successful" |
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| single cell error-lorenzos oil |
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| why do we fall for the single cell error |
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| we assume relationships are perfect |
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| the more vivid something is |
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| the more we are likely to think there is a relationship |
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| a tendency to search for or interpret new information in a way that confirms one's expectations and avoid information that contradicts our expectations |
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These are errors that result from having data in one row (or column) of the contingency table, but not the other
Takes a number of forms, including superstitious behavior |
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| scores in one condition are as high as they can go; no chance to find a higher score in the other condition |
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| Scores in one condition are as low as they can go; no chance to find a lower score in the other condition. |
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| Can’t tell if or what kind of relationship there is when all you know is information from one set of |
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| you cannot tell whether or not there is a relationship simply by knowing the |
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| when we say something is due to chance |
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| we don't mean that it couldn't be predicted or explained (if we knew enough). Rather, we mean that it is caused by (usually many) factors that we are unaware of and/or are unable to measure. |
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the tendency to see links between events in the past and events in the future when the two are really independent
ex)lightening doesnt strike in the same place twice |
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| fall victims to the representative heuristic |
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| Probability judgments are often based on how representative certain features of events are to what we know |
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| Judging that Probability of (A and B) > min (Prob(A), Prob(B)) |
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| people get what they deserve |
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| there is or isn't a relationship |
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| the significance level or the alpha (ά) level |
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| the most unusual 5% of outcomes |
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| the critial regions depend on ά and sample size |
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| the larger the samples, the bigger the critical regions, and hence, the easier it is to conclude that any difference is a significant one. |
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| alpha level states the probability of making one type of mistake (Type I error)= |
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falsely rejecting the null hypothesis;
concluding that there is a difference when there's not |
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| he bigger the chance of making the other kind of mistake |
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| the stronger the relationship is |
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| 3 conditions of causal relationships |
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there is a relationship between A and B
changes in A preceed (in time) changes in B
there is no other third variable, C, which covaries with A |
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| does not imply causation! |
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Definition
as a method in which the investigator creates differences in one and only one variable, A, and then measures a second variable, B.
changes in A are known to precede and changes in B
all other possible causal variables have been controlled (e.g., held constant)
Variable A, the potential cause, which the investigator varies or manipulates, is called the independent variable
Variable B, the possible effect, which the investigator observes or measures, is called the dependent variable |
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| required to establish if there's a relationship; 1st condition |
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| required to establish that the cause has preceded the effect; 2nd condition |
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| required to establish that there are no other, possible causes; 3rd condition |
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Measure the same people on the dependent variable B both before and after the introduction of the purported causal, independent variable A
1 pretest 2treatment 3posttest Time |
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Definition
Take two groups of people, vary (or manipulate) their exposure to levels of the independent variable A, and then measure the dependent variable B
2treatment 3posttest Time
Group I High on IV measure DV
Group II Low on IV measure DV
(compare group means) |
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approach 1 problems:
Any other event besides the independent variable occuring between Times 1 and 3 (in this slice of “history”) could also cause a change. |
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approach 1 problem:
Sometimes, just the passage of time results in people changing, even without any external cause
growing up, growing older, growing stronger, growing weaker, etc. |
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approach 1 problem:
Sometimes, the act of measurement itself at pretest can change behavior at posttest (even without any manipulation of the independent variable) |
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| instrument decay or instrumentation |
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Definition
approach 1 problem:
Sometimes, the measurement instrument changes in a systematic way from pretest to posttest (a systematic bias in measurement), producing apparent differences when there are really none |
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approach 1 problem:
Sometimes, you lose (or gain) people between pretest and posttest, and this change in the composition of the sample itself can produce changes on the dependent variable |
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approach 1:
If there's lots of random error of measurement, people who get especially high (or low) scores at pretest will tend to get less extreme scores at posttest.
If people are selected to be in the study because of the extremity of their scores at pretest, we should expect such changes even without any manipulation
Why? Because the chance factors which make a person especially high at pretest are unlikely to make him/her again especially high at posttest |
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approach 2:
It is possible that the two groups being compared already differed on the dependent variable even before the manipulation was introduced;
i.e., the differences were created in the very act of selection |
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| solving selection problem |
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approach 2:
Better than nothing: Match the two groups on all variables known or suspected to affect the dependent variable
e.g., give half the violent clan TVs and half no TVs; same for the non-violent clan
Why not a perfect fix?
Because you need to know all relevant variables, and be able to measure them all reliably and validly
Good: Get a pre-test on the dependent variable to make sure that the two groups do not differ.
Why not a perfect fix?
Can sometimes get groups that are both extreme but equal at pretest, and regression leads to posttest differences.
Best: Use random assignment to decide which people go into which conditions |
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Definition
Means every person has an equal chance to end up in each group or condition being compared
Idea is that the two groups should not, on average, differ much on any “subject/person” variable (e.g., demographics, personality, prior history) when assignment is left to chance
The bigger the sample sizes, the better it works
Doesn't guarantee that the groups are equal to begin with; rather, just makes it likely that they don't differ much |
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| what makes a real experiment good? |
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Definition
Necessary condition 1: Manipulation.
An experimenter creating differences, rather than simply observing naturally occuring ones.
(If Approach 2 is used) Necessary condition 2: Random Assignment.
Since Selection is always a threat
This means that since you can't make strong causal inference without a (good) experiment, one way to know whether research evidence justifies a causal inference is to see if these two conditions have been met
Ask
was the purported causal variable actually manipulated/varied by the experimenters
were the groups being compared actually assigned randomly to their conditions
If the answer to either question is “No”, causal inference is risky* |
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| common threats of quality of experiments |
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Treatment confounds
Experimenter effects
Demand characteristics
Weak/invalid manipulations |
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| Where the experimenter has created differences not just on the independent variable, but other variables too |
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| The experimenter can sometimes create what s/he expects to see (knowingly or unknowingly) |
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| how can experiment effects be avoided? |
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Do “double blind” experiments, where
the participant is “blind” as to which condition s/he is in
investigator/experimenter is “blind” (uninformed) as to which condition each participant is in
Also have experimenters blind/uninformed as to the hypothesis being tested |
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| These are clues which tell subjects (correctly or incorrectly) what the experimenter is studying and what s/he expects to find. Sometimes this alters subjects' behavior unnaturally. |
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| how can demand characteristics be avoided? |
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Definition
by making the true purpose of the experiment unclear
this can create new, ethical problems (of deception)
e.g., Milgram’s classic obedience studies
Ss led to believe that they were actually delivering painful shocks (when they weren’t)
was highly stressful for many participants
experimenters are often on the horns of dilemmas—they can’t solve one problem without creating another problem |
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| null results look out for |
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ceiling/floor effects
weak manipulation ("restriction of range")
invalid manipulation of ind. variable |
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Definition
If scores on dep. var. in one condition are alreay as high (low) as they can go, then no manipulation can make them any higher (lower)
e.g., suppose those exposed to TV never aggress. Can't demonstrate that taking away TV will decrease aggression. |
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| weak manipulatiom ("restriction of range") |
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Definition
If only tiny differences have been created on the ind. var., then we're not surprised at no differences on the dep. var.
e.g., Wouldn’t expect differences in aggression between kids shown 1 hour per day vs. 61 minutes a day of TV, even if there were a strong relationship
If only tiny differences have been created on the ind. var., then we're not surprised at no differences on the dep. var.
e.g., Wouldn’t expect differences in aggression between kids shown 1 hour per day vs. 61 minutes a day of TV, even if there were a strong relationship |
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| invalid manipulation of ind. variable |
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Unless one has really created differences on ind. var., don't expect effect on dep. var (even if A --> B)
e.g., If you give one group TV, but no electricity to run it, you haven’t really created differences on the IV
Requires a manipulation check—a direct measure of the IV
e.g., measure amount of TV watched (IV) to make sure differences created between experimental conditions |
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| Experimenter can estimate probability that each person in population will be included in the sample |
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| a special case--the probability is equal that each person will be included in the sample |
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| Best surveys in private & non-profits: |
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high response rate:
60-70% |
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| Media “quick-turnaround” surveys |
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| Most surveys of public opinion/attitudes |
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high repsonse rate:
40-50% |
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| solutions for "high" refusal rates |
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Definition
Offer incentives for participating (e.g., $) or disincentives for declining (e.g., pester; penalties)
Follow up (mailings, calls, home visits)
Track down missing people
Establish rapport
Use specially trained interviewers
See if those who do respond are demographically representative of the population of interest |
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| with a probability sample |
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| you can also judge just how far off you're likely to be by using your sample to estimate population parameters--you can determine a margin of (sampling) error. |
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| the smaller the margin of error, all else being equal |
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| double barreled questions |
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| questions with 2 or more parts to which one might be responding |
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| directive/biased questions |
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| questions which guide the respondent to certain answers |
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chicken little
the ostrich approach
an owl approach |
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| the "chicken little" approach |
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Definition
Assume that results always will generalize
E.g., evidence that saccharin can cause cancer in rats is excellent evidence that it will cause cancer in humans
A little evidence (“an acorn on the head”) leads to instant generalization (“the sky is falling”) |
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Assume that results will never generalize
E.g., if the evidence of the carcinogenic effects of saccharin are found under conditions that differ in any way from my conditions, assume that it will not generalize
Need lots of research on people like me (a deluge of acorns) before generalizing (getting head out of the sand and doing something) |
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“keep your eyes (and mind) open” to new evidence
Carefully weigh the costs of errors of generalization
Apply the “plausibility” criterion… |
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do not always mean results will NOT generalize to natural conditions:
Lots of counterexamples:
Discovery of antibiotics
Programmed learning/token economies
In fact, often the most _____, UNnatural, basic research turns out to be the most useful
Why?
Knowledge about causal relationships is especially useful
To make causal inferences, experimental methods are needed
Effective experiments require control
Highly controlled environments are invariably unnatural |
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| no info is lost in such summerization |
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| we sometimes summerize a larger number of observations with a few descriptive statistics. all of the following reasons are good reasons to do so EXCEPT |
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| it can produce a summary that is far more precise than the observation that it is based on |
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| which of the following is untrue about the arithmetic mean as a measure of central tendency |
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| less sensitvie to extreme cases |
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| unlike the mean, the median is |
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| less sensitvie to extreme cases |
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| unlike the mean, the median is |
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| it can produce a summary that is far more precise than the observation that it is based on |
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| which of the following is untrue about the arithmetic mean as a measure of central tendency |
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| less sensitvie to extreme cases |
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| unlike the mean, the median is |
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| if i were an advertiser trying to convince buyers that the "average" age of sun city residents is very high, which central tendency would i be least likely to use? |
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| they are not normally distributed |
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| suppose you learn that the scores from exam 1 are negitevely skewed. from this you can conclude that |
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| none is any larger than the other |
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| suppose you learn that the scores from exam 1 are normally distributed. Which measure of central tendency would be the largest? |
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| johns salary went up 10% in 2003 and 5% in 2004. How much did his salary go up in the whole 2003-2004 period? |
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| How many variables does it take to establish a relationship? |
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| testimonial evidence only provides info about one cell of a contingency rule |
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| the biggest problem in relying on testinmonial evidence is that |
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