Null hypothesis statement

In attempting to reach decisions, it is useful to make assumptions or guesses about the populations involved. Such assumptions, which may or may not be true, are called statistical hypotheses and in general are statements about the probability distributions of the populations. A common procedure is to set up a null hypothesis, denoted by which states that there is no significant difference between two sets of data or that a variable exerts no significant effect. Any hypothesis which differs from a null hypothesis is called an alternative hypothesis, denoted by Tfj. 

A statement that the difference between two values is too great to be explained by indeterminate error accepted if the significance test shows that null hypothesis should be rejected (Ha). 

Ohm s law the statement that the current moving through a circuit is proportional to the applied potential and inversely proportional to the circuit s resistance (E = iR). (p. 463) on-column injection the direct injection of thermally unstable samples onto a capillary column, (p. 568) one-taUed significance test significance test in which the null hypothesis is rejected for values at only one end of the normal distribution, (p. 84)... 

A test of the null h)rpothesis that the rates of infection are equal - Hq x jii/hnj = 1 gives a p-value of 0.894 using a chi-squared test. There is therefore no statistical evidence of a difference between the treatments and one is unable to reject the null hypothesis. However, the contrary statement is not true that therefore the treatments are the same. As Altman and Bland succinctly put it, absence of evidence is not evidence of absence. The individual estimated infection rates are jTi = 0.250 and = 0.231 that gives an estimated RR of 0.250/0.231 = 1.083 with an associated 95% confidence interval of 0.332-3.532. In other words, inoculation can potentially reduce the infection by a factor of three, or increase it by a factor of three with the implication that we are not justified in claiming that the treatments are equivalent. 

It is important to note that the conclusion drawn from the observed data is based on a comparison with virtual data that might have been collected in other identical experiments but were never really observed. In fact, a judgement is made on the data rather than directly on the model or hypothesis. No consideration is given to the plausibility of the original hypothesis or specific alternatives. It is an erroneous assumption that the p value is a measure of the validity of the null hypothesis. As noted, p merely makes a statement about the data on the assumption that the hypothesis is valid. 

With the p-value methodology we are rejecting the null hypothesis Hg in favour of the alternative hypothesis Hj, providing the two (one-sided) p-values are < 2.5 per cent. We have then established equivalence and we can talk in terms of the treatments being significantly equivalent. The terminology sounds almost contradictory, but is a correct statement. If either of the two p-values is above 2.5 per cent then the treatments are not significantly equivalent. 

What is the importance of the null and the alternative hypotheses They enable us to link the baseline and alternative condition statements to statistical testing and to numerically expressed probabilities. The application of a statistical test to the sample data during data quality assessment will enable us to decide with a chosen level of confidence whether the true mean concentration is above or below the action level. If a statistical test indicates that the null hypothesis is not overwhelmingly supported by the sample data with the chosen level of confidence, we will reject it and accept the alternative hypothesis as a true one. In this manner we will make a choice between the baseline and the alternative condition. 

A statistical hypothesis denotes a statement about one or more parameters of a population distribution requiring verification. The null hypothesis, H0, designates the hypothesis being tested. If the tested //, is rejected, the alternative hypothesis, llx, must be accepted. When testing the null hypothesis, acceptance or rejection errors are possible. Rejecting the H0 when it is actually true results in a type I error. Likewise, accepting... 

Suppose our interest is in testing whether the population mean was equal to a particular hypothesized value, pg. A hypothesis testing process typically starts with a statement of the null and alternate hypotheses. The null hypothesis can be stated in the following manner ... 

State the null and alternate hypotheses. It is sometimes easier to state the alternate hypothesis first because that is what we would like to conclude at the end of the study. The null hypothesis then covers the remainder of values of the population parameter. The specific statements of the null and alternate hypotheses depend on the type of study and the analysis approach used. We cover many different examples in later chapters. 

Statisticians often use the following terms A null hypothesis is a statement proposed for test and is identified as Hq. The alternative hypothesis, H, is the competing statement regarding the data that is true if the null hypothesis is false. If the null hypothesis is correct, the acceptance region indicates the correct interval of desired confidence level, or 100(1 - a)%, and the critical region is the interval(s) in which the null hypothesis is false. 

Step 1 Formulate the hypothesis statement, which consists of the null (//q) and alternative (7/a) hypotheses. Begin with the alternative hypothesis. For example, the slope /3i is greater in value than the slope 2, that is, //a )8i > 2- On the other hand, the logic microbial reductions for formula MPl are less than those for MP2 that is, //a MPl < MP2. Alternatively, the absorption rate of antimicrobial product A is different from that of antimicrobial product B that is, Hpj. product A f product B. 

By convention, the null hypothesis is the lead or first hypothesis presented in the hypothesis statement so formally, the hypothesis tests are written as... 

Both hypothesis statements reflect the same objective, but there are significant differences in the decision criterion utilized in each hypothesis. The null hypothesis of case I assumes that the well is producing 100 or more barrels per day unless statistical evidence proves otherwise, resulting in rejection of Hq. The null hypothesis of case II assumes that the well production is inferior unless production records indicate that daily output is more than 100 barrels per day, which will result in rejection of Hq. Both tests are valid and are called one-tailed hypothesis tests under a given type I error. Consider again the original data with a = 0.05. Table 3 summarizes the calculations for the significance tests associated with cases I and II. 

A hypothesis statement should be accompanied by a confidence interval. A null hypothesis could be that the mean consumption of petroleum has remained unchanged over the last 5 yr at a 95% confidence level. 

Rejecting the null hypothesis is equivalent to accepting the alternative hypothesis—that the two populations are unequal. Accepting the null hypothesis is equivalent to accepting the statement accepting that the mean world temperature was not the same in 1950 and in 2010. 

Much of Statistics is concerned with statistical analysis that is mainly founded on statistical inference or hypothesis testing. This involves having a Null Hypothesis (Ho) which is a statement of null effect, and an Alternative Hypothesis (Hi) which is a statement of effect. A test of significance allows us to decide which of the two hypotheses (Ho or Hi) we should accept. We say that a result is significant at the 5% level if the probability that the discrepancy between the actual data and what is expected assuming the null hypothesis is true has probability less that 0.05 of... 

A similar method can be used to compare two mean values, xi and xz from samples with sizes and respectively. The null hypothesis that these two means are not significantly different is equivalent to the statement that (jci —xz) is not significantly different from zero. So eqn [16] can be adapted to give... 

A crucial first step in any statistieal test is the formulation of a hypothesis, i.e., an appropriate wording of the question we wish to ask about the data. The outcome of a statistical test is never a hard fact but rather a statement about the probability of the validity of a formulated hypothesis. A null hypothesis (Hq) is a hypothesis that corresponds to a presumed default state, e.g. that an... 

Hypothesis Test To formulate a statistical test, usually some theory has been proposed. The question of interest is simplified into two competing hypotheses (claims), the null hypothesis H, and the alternative hypothesis Hj, that are not treated on an equal basis since special consideration is given to the null hypothesis. Thus, the outcome of a hypothesis test is either reject H, in favour of Hj or do not rej ect H, the result of a statistical hypothesis test is never reject Hj and in particular is never accept Hj . The result do not reject H, does not necessarily mean that Hg is true, it only suggests that there is not sufficient evidence against H, in favour of Hj the result reject Hg does, however, suggest that the alternative hypothesis Hj may be true. The hypotheses are often statements about population parameters like expected mean value and variance. 

Hypothesis testing is used in the experimental research if the aim of the experiment is to determine whether the difference between two characteristics, such as two means or two standard deviations, is caused by controlled changes in independent variables or to examine the significance of correlation between two sets of data. In statistical terms, hypothesis is a statement about the relationship between two statistical parameters. It includes a null hypothesis, usually stating that two parameters are equal, which is tested against an alternative hypothesis that they are not. Table 1.4 summarizes the equations and the rules for making the dedsion in favour of one of the hypotheses. 

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