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Z Test & T Test PRESENTED BY : GROUP 1 MD SHAHIDUR RAHMANROLL# 003 MD AMINUL ISLAMROLL# 007 MRS ROZINA KHANAMROLL# 038.

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Presentation on theme: "Z Test & T Test PRESENTED BY : GROUP 1 MD SHAHIDUR RAHMANROLL# 003 MD AMINUL ISLAMROLL# 007 MRS ROZINA KHANAMROLL# 038."— Presentation transcript:

1 Z Test & T Test PRESENTED BY : GROUP 1 MD SHAHIDUR RAHMANROLL# 003 MD AMINUL ISLAMROLL# 007 MRS ROZINA KHANAMROLL# 038

2  Sometimes measuring every single piece of item is just not practical  Statistical methods have been developed to solve these problems  Most practical way is to measure a sample of the population  Some methods test hypotheses by comparison  Two most familiar statistical hypothesis tests are :  T-test  Z-test Cont’d

3  Z-test and T-test are basically the same  They compare between two means to suggest whether both samples come from the same population  There are variations on the theme for the T- test  Having a sample and wish to compare it with a known mean, single sample T-test is applied Cont’d

4  Both samples not independent and have some common factor (geo location, before - after), the paired sample T-test is applied  Two variations on the two sample T-test:  The first uses samples with unequal variances  The second uses samples with equal variances

5  Use a Z-Test when you know the mean (µ) of the population we are comparing our sample to and the standard deviation (  ) of the population we are comparing our sample to.  Use T-test for dependant samples when subjects tested are matched in some way or use T-test for independent samples when subjects are not matched.

6 The Z-test compares the mean from a research sample to the mean of a population. Details (μ, σ) of the population must be known. The t-test compares the means from two research samples. Used when the population details (μ, σ) are unknown.

7  A T-test is a statistical hypothesis test  The test statistic follows a Student’s T- distribution if the null hypothesis is true  The T-statistic was introduced by W.S. Gossett under the pen name “Student”  T-test also referred to as the “Student T-test”  T-test is most commonly used Statistical Data Analysis procedure for hypothesis testing  It is straightforward and easy to use  It is flexible and adaptable to a broad range of circumstances Cont’d

8 T-test is best applied when:  Limited sample size (n < 30)  Variables are approximately normally distributed  Variation of scores in the two groups is not reliably different  If the populations’ standard deviation is unknown  If the standard deviation is known, best to use Z-test Cont’d

9 Various T-tests and two most commonly applied tests are :  One-sample T-test : Used to compare a sample mean with the known population mean.  Paired-sample T-tests : Used to compare two population means in the case of two samples that are correlated. Paired sample t-test is used in ‘before after’ studies, or when the samples are the matched pairs, or the case is a control study.

10  Data sets should be independent from each other except in the case of the paired-sample t- test  Where n<30 the t-tests should be used  The distributions should be normal for the equal and unequal variance t-test  The variances of the samples should be the same for the equal variance t-test Cont’d

11  All individuals must be selected at random from the population  All individuals must have equal chance of being selected  Sample sizes should be as equal as possible but some differences are allowed

12 Assumptions: Matched pair, normal distributions, same variance and observations must be independent of each other. Steps in the calculation: 1. Set up hypothesis: Two hypotheses H 0 =Assumes that mean of two paired samples = H 1 =Assumes that means of two paired samples  2. Select the level of significance: Normally 5% 3. Calculate the parameter: t = d /  s 2 / n, n-1 is df 4. Decision making: Compare calculated value (cv) with table value (tv). If cv  tv, reject H 0, If cv  tv, accept H 0 and say that there is no significant mean difference between the two paired samples in the paired sample t-test.

13  The Z-test is also applied to compare sample and population means to know if there’s a significant difference between them.  Z-tests always use:  Normal distribution  Ideally applied if the standard deviation is known Cont’d

14 Z-tests are often applied if :  Other statistical tests like t-tests are applied in substitute  Incase of large samples (n > 30)  When t-test is used in large samples, the t-test becomes very similar to the Z-test  Fluctuations that may occur in t-tests sample variances, do not exist in Z-tests

15  Data points should be independent from each other  Z-test is preferable when n is greater than 30  The distributions should be normal if n is low, if n>30 the distribution of the data does not have to be normal  The variances of the samples should be the same Cont’d

16  All individuals must be selected at random from the population  All individuals must have equal chance of being selected  Sample sizes should be as equal as possible but some differences are allowed

17 Question #1: Does the research sample come from a population with a known mean? Example: Does prenatal exposure to drugs affect the birth weight of infants? Question #2: Is the population mean really what it is claimed to be? Examples: Does this type of car really run 12 kpl? Does this diet pill really let people lose an average of 25 pounds in 6 weeks?

18 Research question: Do Dhaka College students differ in IQ scores from the average college student of BD? Data : National average,  = 114,  = 15, N=150, X = 117 Steps in Calculation: 1. Set null and alternative hypothesis:(From data)  H 0 :  = 114, mean of the population from which we got our sample is equal to 114.  H 1 :   114, mean of the population from which we got our sample is not equal to 114. 2. Select level of significance, generally 5% 3. State decision rules : If z obs -1.96, reject H 0 4. Compute standard error of mean:  x =  /  N = 1.225 5. Calculate z-value: z = X - µ /  x = + 2.45 Cont’d

19 6. Compare observed z to decision rules, and make decision to reject or not reject null.  2.45 > 1.96, so reject H 0. so, more likely that the sample mean is from some other population.  Statistically significant difference between sample mean and the population mean. 7. If H 0 rejected, compare sample mean, and make a conclusion about the research question:  Observed mean was statistically significantly greater than the population mean we compared it to 117 > 114.  So, it can be concluded that Dhaka College students have higher IQ test scores than the average college students of BD.

20  Z-test is a statistical hypothesis test that follows a normal distribution while T-test follows a Student’s T- distribution.  A T-test is appropriate when handling small samples (n 30).  T-test is more adaptable than Z-test since Z-test will often require certain conditions to be reliable. Additionally, T-test has many methods that will suit any need.  T-tests are more commonly used than Z-tests.  Z-tests are preferred than T-tests when standard deviations are known.

21 Q & A


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