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Hypothesis testing Research II Class 5 The logic of hypothesis testing Start with an example: We have a representative sample (400) of primary school children in TinSuiWai Average self-esteem: 30 All primary school children in HK: 32 Question: Is TinShuiWai students different from HK students? The logic is we assume they are equal in the first place Calculate the probability of sampling distribution of mean based on Central Limit Theorem See if 32 is very unlikely If so, reject the assumption (null hypothesis that they are equal) SE = 4/20 (0.5) 95% between 30 +/- 1.96 x 0.5 (29.02 and 30.98) 32 is outside 95% of cases, so very unlikely Reject the null hypothesis H0: There is no difference between the mean self-esteem score of all primary school children in TinShuiWai with that of the primary school children in the general population H1: There is difference between… OR H0: µ (TinShuiWai) = 32 H1: µ (TinShuiWai) ≠ 32 Where µ is the mean self-esteem score. Why should we use this indirect method? Because the null hypothesis is unique and parameters are fixed. The null hypothesis is the statistical hypothesis, which differs from the theoretical hypothesis What explain the difference between the levels of self- esteem among students? A possible answer “Class performance accounts for the different levels of self-esteem among students” This is theoretical hypothesis We have confidence if we have more evidence. If we find counter-evidence, we have to reject the hypothesis and look for other possible answers Designs to test this hypothesis Collect a sample of school-children in HK, divide the students two groups, one is above average performance in their class, another below it. Then we compare whether those with better class performance has a higher level of self-esteem than those lower. Based on the same sample, try to see if self-esteem scores correlate with performance in their class (for example, what percentile their performance is in class). Get a sample of students and randomly assign them into two groups, one of them were given a proven “learning performance improvement training” (suppose there is one), the other serves as a control group. This is a Randomized Clinical Trial (RCT). Then we run the training programme, and after the completion of the programme, we try to find out whether there is an improvement in their self-image (suppose we are quite certain that the training programme improved their class performance). Method 1 Divide the sample into two groups, one with higher level of class performance, one with less Use t-test H0: There is no difference in the average self-esteem score between those with better and worse class performance among the school children in HK H1: There is difference between…… OR H0: µ(better class performance) =µ(worse class performance) H1: µ(better class performance) ≠ µ(worse class performance) Difference in self-esteem Theoretical hypothesis Class performance made a difference Statistical hypothesis H0 H1 Type I error (α) is the probability of rejecting Ho when it is in fact true. Type II error (β) is the probability of not rejecting Ho when it is in fact false. One sample t-test Research question: Does the population’s trust towards social workers differ from the average level, which equal to 6 on a 0-10 scale? Null hypothesis: The population’s mean value of trust towards social workers is equal to 6 Alternative hypothesis: The population’s mean value of trust towards social workers differs from 6. One-Sample Statistics N Mean Std. Deviation Std. Error Mean 社工 503 6.29 1.855 .083 One-Sam ple Test Test Value = 6 95% Confidence Interval of the Difference t df Sig. (2-tailed) Mean Difference Lower Upper 社工 3.462 502 .001 .286 .12 .45 If the null hypothesis is true, that is the population score of the perception towards social workers is 6, then the chances of having the current level of differences (might it be positive or negative) is 0.01 only. We are 99% confident that the sample mean differs from the population mean at this magnitude. In fact, if the population mean was 6, the value of 6.29 will have 95% chances greater than the sampling mean of the population (with true population mean equal to 6) between 0.12 and 0.45. Testing the differences about two related means Research question: Does the population’s trust towards social workers differ from that of lawyers? Null hypothesis: There is no difference between the population’s mean value of trust towards social workers and lawyers. Alternative hypothesis: The population’s mean value of trust towards social workers differs from that of lawyers. Paired Samples Statistics Mean N Std. Deviation Std. Error Mean Pair 1 社工 6.29 503 1.855 .083 律師 5.96 503 2.023 .090 Paire d Sam ple s Te st Pa ire d Diffe rences 95% C onfidence Inte rval of the Diffe rence Mea n Std. Dev iation Std. Error Me an Lowe r Uppe r t df Sig. (2-taile d) Pa ir 1 社工 - 律師 . 330 2. 392 . 107 . 120 . 540 3. 094 502 . 002 We reject the null-hypothesis because the chance of having a sample with difference of 0.33 (in magnitude) is less than 0.02. If the null hypothesis is true (that the two perceptions are being the same, i.e. the difference is 0) the value of 0.33 will have 95% chances greater than the sampling mean of the population (with true population difference equal to 0) between 0.12 and 0.54. Testing the differences between two samples Research question: Does male and female have a different level of trust towards social workers? Null hypothesis: Male and female have the same mean value of trust towards social workers. Alternative hypothesis: Male and female have a different mean value of trust towards social workers. Group Statistics 性別 N Mean Std. Deviation Std. Error Mean 社工 男 230 6.30 1.825 .120 女 273 6.27 1.883 .114 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval Std. Error of the Difference F Sig. t df Sig. (2-tailed) Mean Difference Difference Lower Upper 社工 Equal variances assumed .836 .361 .152 501 .879 .025 .166 -.301 .352 Equal variances not assumed .153 491.308 .879 .025 .166 -.300 .351

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null hypothesis, hypothesis testing, alternative hypothesis, test statistic, type I error, hypothesis test, sample mean, significance level, population mean, type II error

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posted: | 4/24/2010 |

language: | English |

pages: | 26 |

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