probability and statistics concepts
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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| Discrete | Finite number
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| Continuous | Infinite without gaps
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| Nominal | Categories
No order
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| Ordinal | Ordered but difference between is meaningless
Relative comparison
Ex:grades
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| Interval | Ordered but meaningful
Does not start at 0
Ex:temp
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| Ratio | Ordered/meaningful
Starts at 0
Ex:distance
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| Systematic sample | Start point
Select every Kth element
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| Convenience sample | Easy to collect
Close to researchers location
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| Stratified sample | Subgroups (2 of them)
Same characteristics
Draw same amt of sample from each
Consistent
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| Cluster sample | Divide into groups
Select only some groups
Choose all elements from selected group
Faster and less expensive
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| Multistage sample | Combination of methods
Select sample in each stage
Each stage different method
Natural clusters
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| Reason for Frequency Tables | 1)summarize large data
2)analyze nature
3)basis for graphs
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| Relative Frequency | (Class frequency/sum of all frequency)x 100%
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| Unusual Center | Mean-2s or mean+2s
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| Coefficient of variation | (s/x)*100%
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| Bimodal | 2 modes
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| Multimodal | 2+ modes
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| Midrange | (max # - min#)/2
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| Percentile | L(position)= k(percent)/100 *n
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| Interquartile | Q3-Q1
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| 5 Number Summary(mon,q1,med,q3,max) | 1-Vars Stats
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| Odds against | P(not A)/P(A)-> A:B
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| Payoff odds | Net profit: amount of bet
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| Addition Rule of Probability | P(A or B)= P(A) + P(B) /total outcomes
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| Complements | P(none)= 1 - P(at least one)
P(at least one) = P(only A or only B or both)
= P(A only) + P(B only) - P(both)
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| Multiplication Rule (Independent) | P(A and B) = P(A) * P(B)
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| Multiplication Rule (Dependent) | P(A and B) = P(A) * P(B/A)
after event A has occurred
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| Conditional Probability (Independent) | P(B/A) = P(A and B) / P(A)
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| Bayes' Theorem | P(A)*P(B/A) / [P(A)*P(B/A)]+[P(no A)*P(B/no A)]
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| Fundamental Counting Rule | m*n ways
P(A) = 1/m*n
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| Permutation(different) | nPr
n = # of items
r = amt selected
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| Permutation(identical) | nPr = n!/ n1!n2!nk!
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| Combination Rule | nCr
no repeats
no order
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| Requirements for Probability Distribution | 1)Sum of P(x) = 1
2)0 < P(x) < 1 for every x
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| Probability mean | Sum of x * P(x)
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| Probability standard deviation | Square root of Sum of [(x^2 * P(x0]- mean^2
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| Unusual Probability | P(x or more) < 0.05
P(x or fewer)< 0.05
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| Binomial Distribution Requirements | 1)fixed # of trials
2)independent
3)2 categories
4)P(success)same in all success
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| Binomial Probability | binompdf(n,p(success),x success)
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| Binomial Mean | n*p(success)
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| Binomial Standard Deviation | sq. root of n*P(success)*P(failure)
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| Unusual values for Binomial | mean - 2stan. dev
mean + 2stan. dev
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| Poisson Distribution Requirements | 1)x = event of interval
2)random
3)independent
4)uniformly distributed
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| Poisson Standard Deviaton | sq. root of mean
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| Using Poisson as Binomial Distribution Requirements: | 1)n > 100
2) np < 100
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| Poisson Probability | poissonpdf(mean,x selected)
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| Normal Distribution Characteristics | 1)bell-shape
2)mean = 0
3) s = 1
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| Uniform Distribution Characteristics | 1)area = 1
2) correspondence between area and prob
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| Normal Distribution (Area under graph) | normalcdf(left z,right z)
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| Z-score(normal distribution) | invNorm(area left of z-score)
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| Finding P(individual value) w/ Norm Distr | z = x - mean/ stan. dev
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| Finding P(sample) w/ Norm Distr | z = x - mean/ (stan dev./sq. root of n)
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| mean & x to z-score | normalcdf(left, right, mean, s)= P(x)
invNorm(P(x))= z-score
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| Find x value of nonstandard norm distr | invNorm(area to left, mean, s)
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| Sample Variance | Sum(x - mean)^2 / n -1
mean = sum of x/n
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| Normal Distr As Binomial Approximate Requirements | 1)independent simple random sample
2)np> 5 and nq>5
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| Continuity Correction | x - 0.5 to x + 0.5
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| P(Area to left) | normalcdf(-99999,z-score)
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| Normal Distribution on Graph | 1)straight line
2)no systematic pattern
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| Find Critical Value(z-score) | 1-(confidence interval/2)-->invNorm(1-alpha)
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| Margin of Error (z-score) | z(alpha/2) * sq. root(p(success)*q(failure)/n)
or
upper CI - lower CI/ 2
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| Confidence Interval(z- score) | Stat--> 1-PropZInt
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| P(Success) | upper CI + lower CI/ 2
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| Sample Size(independent) | n = (z(alpha/2)^2 *p*q)/E^2
or n = (z(alpha/2)^2 *p*q*.25)/E^2
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| Margin of Error(stan. dev known) | ZInterval
Set mean = 0
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| Sample Size(stan dev known) | n= [z(alpha/2)*stan.dev/E]^2
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| t statistic | invT(1-alpha,df=n-1)
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| Confidence interval(t-score) | TInterval
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| T-Score Properties | 1)norm distr
2)different t for different n
3) mean = 0
4)stan. dev. > 1
5)n increase, t --> norm distr
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| Chi-Square Distribution Properties | 1)not symmetric
2)positive values
3)different for each df
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| Finding Chi-Square | 1)calculate alpha and df
2)What kind of test?
3)Look at Tables given
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| Confidence interval(chi-square) | sq.root[(n-1)s^2/chi right] < stan. dev < sq. root[(n-1)s^2/chi left]
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| Reject null (p-value) | p-value < alpha
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| Find p-value | normalcdf(left, right)
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| Reject null (test statistics) | test statistic falls in critical region bounded by critical value
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| Reject null(confidence interval) | Confidence interval does not contain claimed value
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| Type 1 Error | null true --> reject (alpha)
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| Type 2 Error | null false --> fail to reject (beta)
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| Two Tail Test | null =
alternate not =
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| Right Tail Test | null =
alternate >
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| Left Tail Test | null =
alternate <
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| Testing Claim of Proportion | 1-PropZTest
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| Test Claim on Mean (stan. dev known) | Z-Test
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| Test Claim on Mean (stan dev Unknown) | T-Test
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| Test on 2 Proportions | 2-PropZTest
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| Confidence Interval(2 Proportions) | 2- PropZInt
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| Test on 2 Means (stan. dev. unknown/ independent) | 2-SampTTest
2-SampTInt
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| Test on 2 Means(Stan dev known) | 2-SampZTest
2-SampZInt
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| Claim on Mean (Dependent/differences) | 1) L1 - L2
2)TTest
3)TInt
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| Compare Variation of 2 Samples | 2-SampFTest
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| Correlation | 1)Straight-line
2) r = LinRegTTest
3) r > critical value of alpha
4) reject null
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| Regression | LinRegTTest
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| marginal change | slope of regression line
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| Residual | observed y - predicted y
y from table - y from regression line
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| Coefficient of determination | r^2
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