Statistics for the Social Sciences

95% confidence level

there is a .95 probability that a specified interval DOES contain the population mean. 5 chances out of 100 that the interval DOES NOT contain the population mean

sampling distribution of the mean

theoretical probability distribution of sample means that would be obtained by drawing from the population all possible samples of the same size

99% confidence level

there is 1 chance out of 100 that the interval DOES NOT contain population mean

the standard normal curve

-68% of sample plus or minus 1 standard error of the true population mean -95% of sample falls within plus or munis 1.96 standard errors of the true population mean - 99% of sample mean falls within plus or minus 2.58 standard errors of the true population mean

standard error of the mean

the standard deviation of the sampling distribution. Describes how much dispersion there is in the sampling distribution, or how much variability there is in the value of the mean from sample to sample

standard error of the mean

the standard deviation of the sampling distributions. Describes how much dispersion there is in the sampling distribution, or how much variability there is in the value of the mean from sample to sample

central limit theorem

If all possible random samples of size N are drawn from a population with mean y and a standard deviation, then as N becomes larger, the sampling distribution of sample means becomes approximately normal The Size of the Sample: Although there is no hard-and-fast rule, a general rule of thumb is that when N is 50 or more, the sampling distribution of the mean will be approximately normal regardless of the shape of the distribution. However, we can assume that the sampling distribution will be normal even with samples as small as 30 if we know that the population distribution approximates normality. Since the sampling distribution is theoretical, how can we know its shape and properties so that we can make these comparisons? Our knowledge is based on what the Central Limit Theorem tells us about the properties of the sampling distribution of the mean. We know that if our sample size is large enough (at least 50 cases), most sample means will be quite close to the true population mean. As the sample size gets larger, the standard error of the mean (the standard deviation of the sampling distribution of the mean) decreases in size. The standard error of the mean tells how much variability in the sample estimates there is from sample to sample. The smaller the standard error of the mean, the closer (on average) the sample means will be to the population mean. Thus, the larger the sample, the more closely the sample statistic clusters around the population parameter. -even if a population distribution is skewed, we know that the sampling distribution of the mean is normally distributed -as sample increases, the mean of the sampling distribution becomes equal to the population mean -as the sample size gets larger, the standard error of the mean decreases in size (which means that the variability in the sample estimates from sample to sample decreases as N increases)

standard error

the mean makes it possible to state the probability that an internal around the point estimate contains the actual population mean

normal distribution

a bell-shaped and symmetrical theoretical distribution, with the mean, the median, and the mode all coinciding at its peak and with frequencies gradually decreasing at both ends of the curve

standard deviation

a measure of variation for interval-ratio variables; it is equal to the square root of the variance

variance

a measure of variation for interval-ratio variables; it is the average of the squared deviations from the mean

probability sampling

a method that enables the researcher to specify for each case in the population, the probability of its inclusion in the sample. Used to select a sample that is as representative as possible of the population

sampling distribution

a normal distribution whose mean and standard deviation are unbiased estimates of the parameters and allows on to infer the parameters from the statistics. GENERALIZE FROM THE SAMPLE TO THE POPULATION

estimation

a process whereby we select a random sample from a population and use a sample statistic to estimate a population parameter

confidence interval (CI)

a range of values defined by the confidence level within which the population parameter is estimated to fall. AKA margin of error

simple random sampling

a sample designed in such a way as to ensure that (1) every member of the population has an equal chance of being chosen and (2) every combination of N members has an equal chance of being chosen

point estimates

a sample statistics used to estimate the exact value of a population parameter

standard z scores

express the difference between any score in a distribution and the mean in terms of standard scores. The number of standard deviations that a given raw score is above or below the mean

sample mean

the point estimate of the population

standard deviation

the point estimate of the population standard deviation

margin of error

the radius of the confidence interval

sampling error

the discrepancy between a sample estimate of a population parameter and real population parameter

confidence level

the likelihood, expressed as a percentage or a probability, that a specified interval will contain the population parameter

population distribution

variation in the larger group that we want to know about

distribution of sample observations

variation in the sample that we can observe