Presentation on theme: "Presentation on Data Analysis"— Presentation transcript:
1Presentation on Data Analysis Z Test & T TestPRESENTED BY : GROUP 1MD SHAHIDUR RAHMAN ROLL# 003MD AMINUL ISLAM ROLL# 007MRS ROZINA KHANAM ROLL# 038
2IntroductionSometimes measuring every single piece of item is just not practicalStatistical methods have been developed to solve these problemsMost practical way is to measure a sample of the populationSome methods test hypotheses by comparisonTwo most familiar statistical hypothesis tests are :T-testZ-testCont’d
3Introduction Z-test and T-test are basically the same They compare between two means to suggest whether both samples come from the same populationThere are variations on the theme for the T-testHaving a sample and wish to compare it with a known mean, single sample T-test is appliedCont’d
4IntroductionBoth samples not independent and have some common factor (geo location, before - after), the paired sample T-test is appliedTwo variations on the two sample T-test:The first uses samples with unequal variancesThe second uses samples with equal variances
5When to use Z-Test and T-Test 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.
6Comparing Z-test and t-test The Z-test compares the mean from a researchsample to the mean of a population. Details(μ, σ) of the population must be known.The t-test compares the means from tworesearch samples. Used when the populationdetails (μ, σ) are unknown.
7T-test A T-test is a statistical hypothesis test The test statistic follows a Student’s T-distribution if the null hypothesis is trueThe 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 testingIt is straightforward and easy to useIt is flexible and adaptable to a broad range of circumstancesCont’d
8T-test T-test is best applied when: Limited sample size (n < 30) Variables are approximately normally distributedVariation of scores in the two groups is not reliably differentIf the populations’ standard deviation is unknownIf the standard deviation is known, best to use Z-testCont’d
9T-test 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.
10Data types can be analysed with T-tests Data sets should be independent from each other except in the case of the paired-sample t-testWhere n<30 the t-tests should be usedThe distributions should be normal for the equal and unequal variance t-testThe variances of the samples should be the same for the equal variance t-testCont’d
11Data types can be analysed with T-tests All individuals must be selected at random from the populationAll individuals must have equal chance of being selectedSample sizes should be as equal as possible but some differences are allowed
12Sequence of T-Test (Paired Sample) Assumptions: Matched pair, normal distributions, same variance and observations must be independent of each other.Steps in the calculation:1. Set up hypothesis: Two hypothesesH0=Assumes that mean of two paired samples =H1=Assumes that means of two paired samples 2. Select the level of significance: Normally 5%3. Calculate the parameter: t = d / s2 / n , n-1 is df4. Decision making: Compare calculated value (cv) with table value (tv). If cv tv, reject H0 , If cv tv, accept H0 and say that there is no significant mean difference between the two paired samples in the paired sample t-test.
13Z-TestThe 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 distributionIdeally applied if the standard deviation is knownCont’d
14Z-Test Z-tests are often applied if : Other statistical tests like t-tests are applied in substituteIncase of large samples (n > 30)When t-test is used in large samples, the t-test becomes very similar to the Z-testFluctuations that may occur in t-tests sample variances, do not exist in Z-tests
15Data types can be analysed with Z-test Data points should be independent from each otherZ-test is preferable when n is greater than 30The distributions should be normal if n is low, if n>30 the distribution of the data does not have to be normalThe variances of the samples should be the sameCont’d
16Data types can be analysed with Z-test All individuals must be selected at random from the populationAll individuals must have equal chance of being selectedSample sizes should be as equal as possible but some differences are allowed
17Z-test may ask two questions: 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?
18Sequence of Z-Test (One-Sample) 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 = 117Steps in Calculation:1. Set null and alternative hypothesis:(From data)H0: = 114 , mean of the population from which we got our sample is equal to 114.H1: 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 zobs < or zobs > -1.96, reject H04. Compute standard error of mean: x = /N = 1.2255. Calculate z-value: z = X - µ / x = Cont’d
19Sequence of Z-Test (One-Sample) 6. Compare observed z to decision rules, and make decision to reject or not reject null.2.45 > 1.96, so reject H0. so, more likely that the sample mean is from some other population.Statistically significant difference between sample mean and the population mean.7. If H0 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.
20SummaryZ-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) while a Z-test is appropriate when handling moderate to large 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.