Parametric Test -T test.pptx by Dr. Neha Deo

In the given presentation, parametric testing is discussed. This presentation in detail discusses t -testing which is one of the important parametric tests.t testing related basic terms are also given.
The steps in the t-testing are given in detail. Some examples are also given in the given presentation.

1. Parametric tests- t test Dr. Neha Deo

2. TYPES OF STATISTICS

3. Meaning of Hypothesis Hypothesis is a tentative generalization , the validity of which remains to be tested. Hypothesis is a conjectural statement between two or more variables. The research or scientific hypothesis is a formal affirmative statement predicting a single research outcome, a tentative explanation of the relationship between two or more variables.

4. Meaning of Hypothesis Hypothesis guides the thinking process . Hypothesis is a statement temporarily accepted as true in the light of what is known at that time. Hypo + Thesis So it is a lower level thesis. The thing might be converted in to thesis.

5. When to formulate hypothesis In experimental method it is must. In survey method when significance of difference between two groups is to be tested. In correlation study to test whether the correlation is significant or not. Sometimes in historical research also . But it is not compulsory in each & every research.

6. Types of Hypothesis- Hypothesis-types Main Research Positive H1 States that there will be difference Statistical Null H0 States that there will not be any difference or difference will be zero.

7. Types Hypothesis-types Directional Null Positive Non directional Question Hypothesis

8. Some basic terms Parameter-P -Population Statistics-S-Sample Sampling Unit-It is   one of the units selected for the purpose of sampling . Sampling Error= (P-S) Bias-   It is   a systematic tendency which causes differences between results and facts . Sampling Distribution- S1, S2,S3, S4, S5,……..S N M1, M2, M3, M4, M5,…….M N 112, 113, 110, 109, 119,………… Sampling distribution of Mean Standard Error Standard error of the mean- M pop=M+-( SEM × 1.98 )……….0.05 level Mpop =M+-(SEM × 2.58)…………0.01 levle

9. M pop=M+-( S EM × 1.98 )……….0.05 level….95% M pop=M+-( SEM × 2.58 )………0.01 level….99% Confidence intervals SEM=0.5, SEM × 2.58=1.29 Mpop =M+1.29=155+1.29=156.29 Mpop =M-1.29=155-1.29=153.71 153.71……..156.29 M=155, S.D. =10, SEM=0.5, N=400 SEM × 1.98=0.5 × 1.98=0.99 155+0.99=155.99 155-099=154.01

10. What does a parameter mean? What does parametric mean? Parameter - a numerical or other measurable factor forming one of a set that defines a system or sets the conditions of its operation. Parametric — In STATISTICS assuming the value of a parameter for the purpose of analysis. "variables with normal distribution were compared by means of parametric tests"

11. DATA TYPE

12. Central limit theorem The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution. Sample sizes equal to or greater than 30 are often considered sufficient for the CLT to hold. A key aspect of CLT is that the average of the sample means and standard deviations will equal the population mean and standard deviation. A sufficiently large sample size can predict the characteristics of a population more accurately. Standard Deviation of the distribution of means (Standard error) is smaller than the standard deviation of any selected sample.

13. PARAMETRIC TESTS Z Test T Test F Test ANOVA ANCOVA

14. Student’s t distribution In  probability and statistics   Student's  t -distribution  (or simply the  t distribution ) is any member of a family of continuous probability distributions that arise when estimating the mean of a  normally distributed population in situations where the  sample size  is small and the population's  standard deviation is unknown. It was developed by English statistician   William Sealy Gosset under the pseudonym "Student".

15. TWO GROUPS When Groups are large & normally distributed, Use Z test or sigma test. Obtained critical ratio is compared with two values.(0.05 level 1.96 0.01 level 2.58 ) When Groups are small or more accuracy is required, Use t- test Obtained ‘t’ value is compared with values in D-table . DM SEDM t =

16. Standard Error of Mean Standard Error of Mean: As per the central limit theorem, Standard deviation of the distribution of means is always smaller than the standard deviation of one samples' standard deviation Formula of standard error of mean σ SEM= √N

17. ‘ T’ TEST TYPES

18. Degrees of Freedom Degrees of freedom refers  to the maximum number of logically independent values. For Mean: degrees of freedom df = N For Standard Deviation, degrees of freedom df =N-1 For Coefficient of correlation, df =N-2

19. Level of Significance Significance Levels. The significance level for a given hypothesis test is a value for which a P-value less than or equal to  is considered statistically significant . Typical values for levels of significance are are 0.1, 0.05, and 0.01. These values correspond to the probability of observing such an extreme value by chance.

20. Steps of t- test 1. Find the difference between the two Means 2. Find the standard error of the two Means 3.Find the standard error of the difference between the two means (Use appropriate formula) 4. Find out t ratio.

21. Steps of t- test 5 . Find out degrees of freedom 6.Decide the level of significance: o.o1 or 0.05 7 . Compare the obtained t-value with the table value –D table 8.Take the Decision.(Reject or not to reject the null hypothesis) 9.Write down the findings as per the decision taken..

22. t- testing. M1=47, Sigma1=6, N1=N2=50 M2=52, Sigma2=5 DM=5 SEDM=0.707 df =49 t=DM/SEDM=7.07 The table value at 0.01 level of significance & for 49 degrees of freedom=2.68. obtained t value is 7.07 which is greater than the table value. So null hypothesis is to be rejected. So Research hypothesis is to be accepted. Hence there found a significant increase in the post test mean as compared to the pre test mean. Hence the programme was found to be effective.

23. TYPES OF TESTS TWO TAILED TEST Non directional hypothesis. Only difference is significant or not that is tested. ONE TAILED TEST Directional hypothesis. Increase or decrease in the dependent variable is significant or not that is tasted. In this testing for0.05 level see under 0.1 level & for 0.01 level see under 0.02level in the table

24. Examples Two equivalent groups Experimental design Sr. No. Controlled Experimental A B 1 23 24 2 35 37 3 21 25 4 43 47 5 35 35 6 37 39 7 27 29 8 40 40 9 25 27 10 31 33 11 29 28 12 38 39 13 39 43 14 18 25 15 26 28 One group pre post test experimental design Sr. No. Pre Test Post Test 1 39 41 2 50 52 3 40 43 4 32 33 5 60 63 6 51 57 7 35 36 8 29 32 9 58 61 10 41 49 11 38 40 12 53 58 13 54 53 14 37 38 15 41 41 Two independent groups Sr. No Aided Sr. No. Unaided 1 123 1 139 2 120 2 141 3 110 3 124 4 100 4 123 5 111 5 137 6 137 6 95 7 127 7 89 8 134 8 132 9 99 9 117 10 133 10 128 11 113 11 135 12 134 12 100 13 127 13 101 14 128 14 128 15 127 16 141 Q.Find out whether the difference between the means is significant or not

25. How to calculate “t” ratio Manually using calculator Using Microsoft Excel Using Software like SPSS https ://www.graphpad.com/quickcalcs/ttest2/ Using online calculators