stat flashcards
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| show | Subgroup of the population
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| show | Process of selecting sample from population
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| Random sampling | show 🗑
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| Descriptive vs. Inferential Statistics | show 🗑
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| All inferential statistics have the following in common: | show 🗑
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| show | Structured Problem Solving
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| Scientific methods: steps (cyclic) | show 🗑
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| Variable | show 🗑
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| show | its values are manipulated by the researcher, comes first in time
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| show | measured by researcher, follows the IV in time
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| Population | show 🗑
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| show | controlled by researcher
• randomization of subjects to groups
• keep all subjects constant on EV
• include EV in the design of the experiment
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| show | comes first in time but there is no manipulation, analogous to IV.
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| Criterion variable (CV): | show 🗑
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| show | IV causes the DV
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| Predictive relationship: | show 🗑
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| 2 Types of research | show 🗑
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| True experiment | show 🗑
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| show | • no manipulation
• minimal control of EV
• predictive relationship between PV and CV
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| show | • The first digit(s) of a score form the stem, the last digit(s) form the leaf.
• We want 10-20 total number of stems.
• Number of stems per digit depends on total number of stems: can do 1, 2, or 5 stems per digit.
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| show | – Middle
– Spread
– Skewness
– Kurtosis
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| show | central tendency, location, center
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| show | mean, median, mode
• “Middle” is the aspect of data
we want to describe.
• We describe/measure the middle of data in a population with the parameter m (‘mu’); we usually don’t know m, so we estimate it with X-bar.
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| Other words that describe Spread | show 🗑
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| show | range, variance, standard deviation, midrange
• “Spread” is the aspect of data we want to describe.
• Any statistic that describes/measures spread should have these characteristics: it should
– Equal zero when the spread is zero.
– Inc
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| show | =departure from symmetry
– Positive skewness = tail (extreme scores) in positive direction
– Negative skewness = tail (extreme scores) in negative direction
(The Few name the Skew)
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| show | peakedness relative to normal curve
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| show | -The sample mean is the sum of the scores divided by the number of scores, and is symbolized by X-bar, X = SX/N
-For example, for X1=4, X2=1, X3=7, N=3, SX=12 and X = SX/N = 12/3 = 4
• Characteristics:
– X-bar is the balance point
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| Sample Median | show 🗑
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| Sample Mode | show 🗑
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| show | • We describe/measure the spread of data in a sample with the statistics:
– Range = high score-low score.
– Midrange, MR.
– Sample variance, s*².
– Sample standard deviation, s*.
– Unbiased variance estimate, s².
– s.
• We des
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| Midrange (MR) | show 🗑
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| show | ([median position]+1)/2
– [median position] is the whole number part of the median position (remember, median pos.=(N+1)/2)
• Use hinge position to count in from the tails to find the hinges.
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| show | • Definitional formula: s*²=S(X-X)²/N, the average squared deviation from X-bar.
Sample Standard Deviation= s*
Unbiased Variance Estimate, s²
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| show | • A pictorial description that uses a box to show the middle of the data and lines called whiskers to show the tails of a distribution.
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| 3 Parts to Box Plot | show 🗑
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| show | – Upper end is at the UH, lower end is at the LH - Line across the middle is X50
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| show | – Whiskers are lines drawn from the ends of the box (the hinges) to adjacent values, UAV & LAV.
– Adjacent values are the first real data values inside the inner fences.
– Inner fences, upper and lower
• Upper, UIF=UH+1.5MR
• Lower, LIF= L
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| show | Outliers: outside whiskers, marked with
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| Midrange (MR) | show 🗑
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| z Scores | show 🗑
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| Z score formula | show 🗑
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| z score characteristics | show 🗑
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| show | – Symmetric, continuous, unimodal.
– Bell-shaped.
– Scores range from -¥ to +¥ .
– Mean, median, and mode are all the same value.
– Each distribution has two parameters, m and s².
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| Use of Z score | show 🗑
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| show | – Defined as the degree of linear relationship between X and Y. – Is measured/described by the statistic r.
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| show | – Is concerned with the prediction of Y from X Forms a prediction equation to predict Y from X
Uses the formula for a straight line, Y’=bX+a.
– Y’ is the predicted Y score on the criterion variable.
– b is the slope, b=DY/ D X=rise/run.
–
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| show | r=SzXzY/N, the average product of z scores for X and Y
– Works with two variables, X and Y
– -1<r<1, r measures positive or negative relationships
– Measures only the degree of linear relationship
– r2=proportion of variability in Y that is e
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| show | proportion of variability in Y that is explained by X.
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| Correlation: Undefined | show 🗑
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| show | r (rho)
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| regression cont. | show 🗑
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| Line of Best Fit | show 🗑
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| Partition total spread | show 🗑
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| show | Defined as relative frequency of occurence.
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| show | all possible outcomes of an experiment
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| show | a single member of the sample space
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| Event | show 🗑
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| show | 1/(total number)
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| p(event) | show 🗑
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| show | • p(A|B)=(number in [A and B])/(number in B)
• The probability of A in the redefined (reduced) sample space of B.
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| show | 1. independence 2. mulitplication, mutually exclusive 3.) addition
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| Independence (1) | show 🗑
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| show | • p(A and B)=p(A)p(B|A)=p(A|B)p(B)
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| Mutually exclusive: | show 🗑
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| show | p(A or B)=p(A)+p(B)-p(A and B)
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| The sampling distribution of X-bar | show 🗑
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| show | is the process of testing tentative guesses about relationships between variables in populations. These relationships between variables are evidenced in a statement , a hypothesis, about a population parameter.
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| Test statistic | show 🗑
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| Assumptions | show 🗑
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| show | the hypothesis that we test; Ho.
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| Alternative hypothesis | show 🗑
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| show | he standard for what we mean by a “small” probability in hypothesis testing; a.
The significance level is the small probability used in hypothesis testing to determine an unusual event that leads you to reject Ho.
– The significance level is sym
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| show | >,<, or =
• Directional hypotheses specify a particular direction for values of the parameter.
– IQ of deaf children example: Ho: m>100, H1: m<100.
• Non-directional hypotheses do not specify a particular direction for values of the paramet
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| One- and two-tailed tests | show 🗑
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| Critical values | show 🗑
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| show | the values of the test statistic that lead to rejection of Ho
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| show | • Reject Ho if
– ½ the SAS p-value <a, and
– the observed zX is in the tail specified by H1.
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