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Math 101 Reviewer UPM


Hypothesis Testing

I. Introduction Statistical Inference is the procedure of generalizing to the population, the observations found in the sample Statistical inference has 2 areas: Estimation Hypothesis Testing A hypothesis is a statement about one or more populations There are 2 types of hypothesis: Null Hypothesis Alternative Hypothesis

II. What is Hypothesis Testing? Hypothesis Testing comprises those procedures by which it is decided to reject or not a hypothesis Sampling Variation makes sure that any single sample will differ somewhat from the population value Sample values with small deviation from the parameter value are more likely to happen while extreme values are otherwise

III. Steps in Hypothesis Testing The hypothesis must be testable(open for statistical assessment)1. State the null and alternative hypothesis The null hypothesis is the hypothesis of no difference, it is a statement of equality2. State the level of significance the level of significance, alpha, is the probabaility level that is considered too low to warrant support of the hypothesis being tested the experimter is liable to commit one of the two types of errors, namely: Type I Error(alpha error), rejecting a true hypothesis Type II Error(beta error), accepting a false hypothesis when alpha is 0.5, the probability of rejecting a true hypothesis is at most equal to 5% alpha and beta are related inversely (1-beta) is called the power of the test, it is the probability of rejecting a false hypothesis

3. Choose the test statistic and determine the sampling distribution4. Determine the critical region the region of non-rejection is equal to (1 alpha) the critical region is equal to alpha A one tailed test is used if the alternative hypothesis specifies the direction of the predicted difference5. Compute the test statistic6. Make a statisical decision to reject or not reject the null hypothesis, it is rejected if the test statistic falls in the critical region7. Draw conclusions if the null hypothesis is rejected, we conclude that it is not true if the null hypothesis is not rejected, we conclude that the it may not be true the statistical decision should not be interpreted as definitive, and should be considered along with all other reelevant information available to the decision maker

IV. General criteria for test selection Level of Measurement: (nominal & ordinal vs ration & interval) are the observations nominal, ordinal, ratio or interval Objectives /Purposes of the study: (# of samples being compared) trying to determine if a sample could have been from a population with a stipulated mean or a proportion or from a population of some pre-specified distribution comparison of 2 sample means or proportions comparison of more than 2 sample means or proportions determination of correlation or association between variables Design of the Study: (paired or independent) are the samples independent or paired? Assumptions of the Test: (use non-parametric when the assumptions of parametric are not tenable)s parametric or non parametric?

V. Parametric vs Non-parametric1. Parametric Tests Parametric Tests, are statistical tests that are based on the assumption made by concerning the parameters of the population The assumptions which must be satisifed by parametric tests: random selections of sample normal distribution of the population from which the samples were drawn when more than one population is sampled, equality of variances must be satisfied Parametric tests usually involve numerical data measured either in interval or ratio scale2. Non-parametric Tests Non-parametric Tests are defined as tests in which no hypothesis is madeabout specific values of the population parameters Distributon-free Tests are defined as tests in which the hypothesis is tested with no assumptions made by concerning the form of the distribution of the variables This test is used when the researcher is in no position to make any assumptions about the population parameters, or about the form of the distribution, or if he doubts the validity od the parametric assumptions Non-parametric tests usually involve non-numerical data, being nominal or an ordinal scale

VI. The meaning of P-value P-value can be thought as the probability of obtaining a result as extreme or more extreme than the actual sample value obtained given the null hypothesis is true Guidelines for judging significance of P-value: If 0.1 < p