SMCR Kap 1-3

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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