Parametric-and-Non-Parametric

1、Parametric and Non-Parametric,Decision process,Step1: What question do you want to address? E.g Is there a relationship between Age and Grade? Do older people have higher GPA then younger people? Step2: Find the questionnaire items and scales that you need to address Step 3: The nature of each of yo

2、ur variables. Step 4: Produce Descriptive statistics Step 5: Non-Parametric vrs Parametric Step 6: Final decision,Examine 2 approaches Techniques used to explore relationships between variables e.g Chi-square for independence, Correlation (non-parametric alternative Spearmans rank) , Multiple regres

3、sion,Techniques used to explore differences among groups e.g Independent samples t-test (non-parameteric alternative Mann-Whitney Test), One way/Two way between groups analysis of variance (non-parameteric alternative Kruskal- Wallis test),parametric statistical test is one that makes assumptions ab

4、out the parameters (defining properties) of the population distribution(s) from which ones data are drawn, a non-parametric test is one that makes no such assumptions,Non-parametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing

5、Parametric inferential statistical methods are mathematical procedures for statistical hypothesis testing,Parametric Tests - Assumptions,Assume that the sample has been randomly selected from the population it represents and that the distribution of data in the population has a known underlying dist

6、ribution The data is continuous, interval or ratio type data,Distributions,Normal Probability Distribution,Characteristics of the normal probability distribution: Bell-shaped, single peak at the centre of the distribution. The arithmetic mean, median and mode are equal and located in the centre of t

7、he distribution. Thus half the area under the normal curve is to the right of this centre point and the other half to the left of it. It is symmetrical about the mean. The distribution is asymptotic. The curve gets closer and closer to the X-axis but never actually touches it.,Bell Shaped Distributi

8、on,A normal distribution is defined by its mean and standard deviation. In other words, there isnt one normal distribution but a family of normal distributions depending on the value of the mean.,Standard Normal Distribution,We can use one member of the family to determine probabilities for all norm

9、al distributions. We can identify a Standard Normal distribution to which all Normal distributions are related. This has a mean of 0 and a standard deviation of 1.,Standard Normal Distribution,Most normal distributions will not have these characteristics but can be adjusted so that they do. If a nor

10、mal distribution has these characteristics we can use tables of calculated probabilities to see how likely it is for a particular number to occur All normal distributions can be generated from this Standard Normal distribution through Z, which relates the mean and standard deviation of any Normal di

11、stribution to the Standard Normal distribution. A continuous random variable X is one that can assume an infinite number of values within any given interval. The probability that X falls within any interval is given by the area under the probability distribution. The total area under the curve is 1,

12、Z-scores,Suppose we have a data set with a mean of 40 and a standard deviation of 3, we need a mean of 0 and a standard deviation of 1 To convert our data into this format we simply subtract the mean of the data set from each observation Divide each by the standard deviation,Standard Normal Tables,T

13、he area under the standard normal curve between z = 0 and z = 1.96 is obtained by looking up the value of 1.96 in the tables. We move down the z column in the table to 1.9 and then across until we are below the column headed 0.06. The value that we get is 0.4750. This means that 47.50% of the total

14、area (of 1 or 100%) under the curve lies between z = 0 and z = 1.96. Because of the symmetry the area between z = 0 and z = -1.96 is also 0.4750 or 47.5. The table deals with absolute values,Bell Shaped Distribution,Examples,Suppose that X is a normally distributed random variable with mean = 10 and

15、 STDEV=4 and we want to find the probability of X assuming a value between 8 and 12. We first calculate the z values corresponding to X value of 8 and 12 and then look up these z values in the statistical table at the back of the handout.,On the tables for z =1 we get 0.3413. Then z = = 0.6826. This

16、 means that the probability of X assuming a value between 8 and 12 or P (8 X 12) IS 68.26%,Suppose again that X is a normally distributed random variable with mean = 10 and variance = 4. The probability that X will assume a value between 7 and 14 can be found as follows,For = -1.5 we look up 1.50 on

17、 the tables and get 0.4322. For = 2 we get 0.4772. Therefore P (7 X 14) = 0.4332 + 0.4772 = 0.9104 or 91.04%,Univariate and Bivariate,When you study some trait of all the members of a defined population you know (given that you have measured reliably and validly) the “true” value of that trait (such

18、 as the mean circulation rate of all users). When you study some trait of a sample of that population you have an estimate of the “true” value of that trait.,Univariate and Bivariate,Because of sampling error (which will always exist) your estimate of the “true” value of the trait will have some deg

19、ree of error. You can determine the degree of error by conducting a study of the entire populationbut if you could afford to do that you would not being doing a sample!,Univariate and Bivariate,Since we can only afford to do a sample, we infer from our sample results to our population about the “true” value of this trait. The sample results are our best estimate of the “true” population value on this trait. This is called “inferential statistics.”,Nonparametric,Nonparametricstatistics refer to a statistical method w