SMCR Kap 1-3

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• Sampling distribution Scores of multiple samples in a chart, all possible sample statistic values and their probability densities
• Expected value Mean of sampling distribution
• Sample statistic Number describing a characteristic of a sample
• Sampling space All possible sample statistic values
• Probability density Tool to get probability which a numerical random value falls within a particular range
• Random variable Variable with values that depends on chance
• Expected value Mean of probability distribution, such as a SaDi
• Unbiased estimator Sample statistic for which the expected value equals population value (oftentimes mean)
• Statistical inference Generalization from data collected in a random sample to the population from which the sample was drawn
• Probability summing Each probability, and the sum of that
• Probability distribution of sample statistic Sampling space with probability between 1 and 0 for each outcome of the sample statistic
• Discrete probability distribution Only a limited number of outcomes are possible
• Mean of sampling distribution of sample proportion equals: Population proportion
• Representative sample Variables in sample are distributed in the same way as in the population
• Downward biased estimate Estimate too low
• 10% .100 probability
• Left-hand probability Probability of values up to and including a threshold value
• Right-hand probability Probability of values above and including a threshold value
• Samples Cases (units of analysis)
• Sample characteristics Observations
• Population mean Expected value of the SaDi
• Expected value of sampling distribution Average of Sadi
• Sample with replacement Draw the same sample multiple times
• Bootstrapping Sampling with replacement from the original sample to create a SaDi
• Exact approach Calculating true SaDi as the probabilities of combinations of values on categorical variables
• Theoretical approximation Using TPD as an approximation of the SaDi
• Independent samples Samples that can in principle be drawn separately
• Dependent/paired samples Composition of a sample partly or entirely depends on the composition of another sample
• Samling distribution of sample proportion Exact distribution(Binomial), probabilities of each number or proportion can be calculated
• Replacement sampling two yellow candies of 20% (.20x.20) .040, assuming that probability remains the same while sampling
• When do we sample without replacement? Large population, so the probability switch when removing one sample is irrelevant
• Main limitation of Bootstrapping Bootstrapped SaDI may yield a distorted view of the true SaDi, if variables is not more or less distributed as in the population
• Advantages of bootstrapping Getting a SaDi for any sample statistic, more or less only way to get SaDi for median
• Combination column Lists all possible outcomes
• Exact approach baselines Probabilities of each combo have the same outcome, only works with categorical data, the number of observations need to be limited
• Exact approach proportions Based on frequencies, and these are discrete
• Theoretical probability distribution definition Mathematical functions of sampling distributions
• Why TPD? Convenience of researcher
• Population proportion equal to Average of SaDi, because sample proportion is an unbiased estimator of the population proportion
• Rule for using normal distribution as sample distribution Multiply proportions and requiring the result to be larger than 5
• Comparing two means Comparing samples that are statistically independent of each other
• Same measurement in samples for comparing two means Dependent samples
• Conditions of TPD often involves Size of sample, sample time, shape/variance of population dis.
• Condition of TPD not met No SaDi. Use bootstrap or exact tests
• When are samples independent? If we can in principle draw a sample for one group, without taking into account the sample for another group of cases
• Why bootstrap without replacement Sample and bootstrap must be equal size
• Condition for TPD Large sample size, but not as important if the proportion is around .5
• Width of CI Precision
• Critical value x Standard error Exact distance between lowest population value and sample result
• Standard deviation of SaDi Sampling error
• Point estimate Single guess for the population value
• Interval estimate Range of plausible population values
• Confidence level Probability that a sample falls within an interval
• Critical value Value of TPD that separates the top or bottom values (2.5%, -1.96-1.96)
• Confidence interval All plausible population values given the sample we have drawn
• Advantage of unbiased estimator We have no reason to prefer a value higher or lower than the sample as our estimate
• Why estimate range of parameter? A precise parameter is unlikely to appear in a sample
• SaDi of continuous sample statistic gives us Probability of finding a range of scores for the sample statistic in a random sample
• Obtaining lower limit from upper limit Difference between upper limit and mean of distribution, then take the difference and subtract from the mean
• The wider the interval Less precise is our estimate
• Goal of research Find precise estimate from the population value
• Easiest but least useful way of increasing precision Lowering confidence that the estimation will be correct
• Heightening CI Higher frequency of which where the population value can appear
• Increasing sample size Increases precision of interval, as large samples allows for a more precise estimate
• Standard error tells us How precise the interval estimate is going to be
• The bigger the sample The smaller the standard error
• Standard error meaning Reminds us that it is the size of the error we are likely to make if we use the value of the sample statistic as point estimate for population vlaue
• If we know the standard error We know the interval in which we find the 95% of samples that are closest to the population value
• Lowering standard error Narrowing the sampling distribution
• Standardizing sampling distribution Subtract mean of SaDI from each sample mean in the distribution, then divide by standard error
• 1 z-score 1 SD from the mean
• Z-value tells us How close we are to the upper/lower limit
• If we know the population proportion We can calculate an exact probability of getting a sample with a particular proportion
• Dependent samples The composition of a sample depends partly/entirely on the composition of another sample
• Independent samples Samples that can in principle be drawn separately
• The larger the sample More narrow/precise the confidence interval
• F & Chi does not work with SE (standard error) Use of bootstrapping

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