Hypothesis Testing
Sampling Error(estimation error) –a) the difference between a sample statistic and the true population parameter that the sample statistic is being used to estimate. b) the error caused by observing a sample instead of the population, caused by sample-to-sample variation. c) in practice the exact sampling error for a statistic is typically unknown but statistical theory provides procedures for estimating the of the sampling error, called the standard error. d) the likely size of the sampling error can generally be reduced by increasing the sample size, although generally there are also costs involved with larger sample sizes.
Nonsampling Error – a) a catch-all term for the deviations from the true population parameter that are not a function of the sampling error (e.g. poorly worded questions or untruthful respondents). b) much more difficult to quantify than sampling error.
Hypothesis Testing–a) the standard approach to assessing whether an observed value of a variable or an observed relationship between two or more variables derived from sample data is “real,” that is holds true in the population or is a result of mere chance. b) is an inferential statistics approach, that allows the researcher to use characteristics derived from sample data to make inferences about population characteristics. c) involves comparing empirically observed findings with theoretical expected findings. d) estimates the statistical significance of findings. e) involves posing opposing hypotheses about a population characteristic or the relationship between two or more population characteristics and then testing those hypotheses. f) asks how often the observed results could be expected to occur by chance, if the answer is relatively frequently, then chance would remain a viable explanation of the effect but if relatively rarely, then chance would not be a viable explanation.
Null Hypothesis–a) in hypothesis testing it is the claim or statement about a population parameter that is assumed to be valid or true unless the observed data contradicts this assumption. b) the hypothesis that two variables are not related or that two statistics (e.g. means or proportions) are the same. c) symbolized as H0. d) hypothesis test can either reject the null hypothesis, in which case the alternative hypothesis may be true, or fail to reject the null hypothesis.
Alternative Hypothesis (research hypothesis) - a) in hypothesis testing it is the opposite claim or statement about a population parameter from the null hypothesis. b) the hypothesis that two variables are related or that two statistics (e.g. means or proportions) are different. c) the hypothesis that the researcher expects to be supported, although this perspective is controversial. d) symbolized as H1 or HA.
Type I Error (alpha, false positive, false alarm) –a) falsely rejecting a true null hypothesis. b) mistakenly concluding that a difference exists in a population parameter when the sample difference was merely a result of chance. c) considered the more serious form of error and more important error to avoid. d) A court finding a person guilty of a crime that theydid notactually commit.
Type II Error (beta) –a) falsely rejecting a true alternative hypothesis or falsely failing to reject a false null hypothesis. b) the inverse of type I error, so the greater the risk of committing one then the lower the risk of committing the other. c) a court finding a person innocent of a crime that theyactually committed.
Significance Level (alpha level)– a) the probability of making a Type I Error. b) 0.05 is probably the most common significance level and corresponds to a situation in which Type I Error is committed only one time in 20. c) the inverse of the confidence level, so significance level of 0.05 corresponds to a95% confidence level.
Critical Value – a) the points in a test statistic sampling distribution that define a statistically significant result, that is a result unlikely to have occurred merely due to chance. b) the value of a test statistic that result in rejecting or failing to reject the null hypothesis, that is the zone of rejection. c) found in tables for a test statistic (like chi-square , t-test, and z-test) and not calculated from observed data.
Critical Region (Zone of Rejection)– a) the critical region of a hypothesis test is the set of all outcomes which, if they occur, will result in rejecting the null hypothesis.
Degrees of Freedom (df) – a) the number of values that are free to vary or the number of independent pieces of information when calculating a test statistic. b) the number of independent scores or observations used to calculate a test statistic minus the number of statistics estimated as intermediate steps in the estimation of the statistic itself. c) an important but difficult to understand concept in inferential statistics but fortunately one with straightforward practical applications and simple equations.