Some Statistical Tests

Paired Sample T Test

• The Paired Samples T Test procedure compares the means of two variables for a single group. It computes the differences between values of the two variables for each case and tests whether the average differs from 0.
• For administering Paired Samples T Test both the variables should be normally distributed. We can check for normal distribution with Q-Q Plot from Graph menu of the SPSS window.
• The SPSS shows a number of results such as descriptive statistics including mean, satandard deviation and the pair; correlation between the variables including the significance value; and the result of the T Test.
• The Paired Samples T Test is based on the difference between the two variables. Under 'Paired Differences' we see the descriptive statistics for the difference between the two variables.
• To the right of the paired difference we see the T, degrees of freedom, and significance.
• If the T value is 0.601, the degree of freedom 39 and significance 0.552 then we have to conclude that there is no significance difference between the two variables.
• The rule is that if the significance value is less than 0.05, there is a significance difference, and if the value is greater than 0.o5, then we have to conclude that there is no significance difference.

One Way ANOVA

• The One Way ANOVA compares the mean of one or more groups based on the one independent variable (factor)
• While using this statistical tool, move all the dependent variables into the box labeled 'Dependent List' and move the independent variable into the box labelled 'Factor'.
• Click on the botton labelled 'options; and check of the boxes for Descriptive and Homogeneity of the Variance.
• Click 'post hoc' botton, if there are equal number of cases in each group choose 'Tukey' if there are not equal numbers of cases in each group, choose 'Bonferroni'.
• The dependent variables should be normally distributed with a Q-Q plot.
• The between groups estimate of variance forms the numerator of the F ratio. The second row corresponds to the within groups estimate of variance (the estimate of error). The within groups estimate of variance forms the denominator of the F ration
• When the significance value is less than 0.05, then we have to reject the Null Hypothesis since the F value is not statistically significant.
• There are two degrees of freedom. The first one is calculated as a-1 where 'a' refers to number of variables. The second degree of freedom is calculated as a(n-1) where 'n' refers to number of cases to be observed.

Pearson Correlation

• The Pearson R Correlation tells us the magnitude and direction of the association between two variables that are on an interval or ratio scale.
• Both variables should be normally distributed.
• SPSS creates a correlation matrix of the two variables. It gives three pieces of information: the correlation coefficient, the significance, and the number of cases (N).
• The correlation coefficient is a number between +1 and -1. This numbers tells us about the magnitude and direction of the association between two variables.
• The magnitude is the strength of the correlation. +1 indicates the strongest positive correlation whereas -1 indicates the strongest negative correlation. If the correlation is 'zero' or very close to it, it shows that there is no correlation between the variables.
• If the correlation is positive, the two variables have positive relationship (as one increases, the other also increases). If the correlation is negative then it shows that the variables have inverse relationships.

Feedback

There are different factors that affect second language learning. Some of them are age, critical period, motivation, exposure, procedure, etc. Among them feedback is taken as an important factor so far as behaviouristic theory of language learning.
Feed back refers to any information which provides a report on the result of behaviour, commments or information that learners receive on the success of a learning task, either from the teacehr or from other learners.
Reinforcement in Stimulus-Response theory refers to a stimulus which follows the occurance of a response and affects the probability of that response occuring or not occuring again.
Reinforcement which increases the likelihood of response is known as positive reinforcement and reinforcement that decreases likelihood of a response is known as negative reinforcement.
So, it seems that reinforcement is a bit specialized term than feedback.
In the case of second langauge learning feedback plays a vital role.On the one hand it praises and encourages learners to produce correct utterances, and discourages them from making mistakes on the othe hand.
Positive or negative, both of types of feedback help learners to learn better. Positive feedback strenthens the learned linguistic behaviour whereas negative feedback avoids undesired behaviours.
Students expect positive feedback from their teachers.
It is not necessary to give feedback in the case of first language learning because they recieve in one or all of the following ways:

• Parental reward
• Trial and error
• Correct forms provided by adults
• Analogy and generalization

ANOVA

Reference: http://home.ubalt.edu/ntsbarsh/stat-data/Topics.htm

• According to Field (2006), ANOVA refers to a family of statistical procedures that use F-test to test the overall fit of a linear model to the observed data. The result of F-test is an overall test whether group means differ accross levels of the categorical independent variable(s).
• "Simply, if there is one independent variable then the ANOVA is called a one-way ANOVA. If two independent variables have been manipulated in the the research, then a two-way ANOVA could be used to anayse the data." (Field, 2006)

Reference:
Foster, Kelly N., and Leah Melani Christian. " F-Test." Encyclopedia of Survey Research Methods.2008. SAGE Publications. 4 Mar. 2009. http://sage-ereference.com/survey/Article_n197.html.

• Foster and Christian (2008) writes, the F test is frequently associated with analysis of variance (ANOVA) and is most commonly used to test the null hypotheis that the means of normally distributed groups are equal.
• The F test was devised as an extension to the Z-test. Although the F test produces the same information as the Z test, when testing one independent variable with a nondirectional hypothesis, the F test has a distinct advantage over the Z test because multiple independent groups can easily be compared.
• The F test compares the observed value to the critical value of F. If the observed value of F (which is derived by dividing the mean squared error) is larger than the critical vlaue of F (obtained using the F distribution tabel) then the ralationship is deemed statistically significant and the null hypothesis is rejected.
• According to Foster and Christian (2008), there are two types of degree of freedom associated with the F test. The first is derived by subtrcting 1 from the numebr of independent variables and the second by subtracting the number of independent variables from the total number of cases. In output tables from software packages such as SPSS, SAS, and STATA the F value is listed with the degree of freedom and a P value. If the P value is less than the alpha valuechose (e.g. P<.05) then the relationship is statistically significant and the null hypotheis is rejected.

Hypothesis for Small Samples

• When we have a small sample from a normal population, we use the same method as a large sample except we use the t-statistic instead of z-statistic. Hence, we need to find the degrees of freedom (n-1) and use the t-table in the back of the book.
• A z-statistic is usually used for large sample size (n greater or equal to 30) drawn randomly. The population standard deviation is estimated by the sample standard deviation. The t curves are bell shaped and distributed arond t=0. The exact shape on a given t-curve depends on the degree of freedom. In case of performing multiple comparisions by on way Anova, the F-statistic is normally used. The critical value of 'F' is read off from the tables on the F-distrubition knowing the type I error and the degree of freedom betwen and within the groups.

Procedure in Hypothesis Testing

1. Formulate the null hypothesis and alternate hypothesis
2. Choose a level of significance
3. Determine the sample size
4. Collect data
5. Calculate z or t score
6. Utilize the table to determine if the z-score falls within the acceptance region
7. Decide

Data Processing and Analysis

• Data processing implies editing, coding, classification and tabulation of collected data so that they are amenabel to analysis (Kothari, 2004, p. 122).
• Analysis, particularly in case of survery or experimental data, involves estimating the values of unknown parameters of the population and testing of hypothesis for drawing inferences. If the analysis deals with a single variable then it is called descriptive analysis but if it deals with more than one variable then it is called inferential analysis. The latter is also known as statistical analysis.
• There are different types or elements of inferential data analysis. Normally, research have more than one variables to be analysed, the data of such research need multivariate analysis. Usually, the following analyses are involved when we make a reference of multivariate analysis: multiple regression analysis, multiple discriminant analysis, multivariate analysis of variance (multi ANOVA) and canonical analysis.
• Statistics has an important role in designing research, analysisng its data and drawing conlusions. There are two major areas in statistics: descriptive statistics and inferential statistics.
• Descriptive statistics concern the developmetn of certain idices from the raw data, whereas inferential statistics concern with the process of generalization. The latter is also known as sampling statistics and are mainly concerned with two types of problems: the estimation of population parameters and the testing of statistical hypotheses.
• The important statistical measures to summarize the survey/research data are: measures of central tendency or statistical averages, measures of dispersion, measures of asymmetry (skewness), measures of relationship and other measures.
• Mean is the simplest measurement of central tendency and is widely used measure (Kothari). Its chief use consists is summarizing the essential features of a series and in enabling data to be compared.
• Standard deviation is most wiely used measure of dispersion of a series. It defined as the square-root of the average of squares of deviations, when such deviations for the values of individual items in a series are obtained from the arithematic average.
• Skewness is an important tool to measure asymmetry of the data. It shows the manner in which the items are clustered around the average. A normal curve shows normal distribution of the data and it indicates there is no skewness. If the curve is distorted on the right side, we have positive skewness but when it is distorted on the left side it is called negative skewness.
• There are different methods of determining the relationship between two variables. Mainly there are two questions to be answered:

1. Does there exist association or correlation between the two or more variable? If yes, of what degree?
2. Is there any cause and effect relationship between the two variables? If yes, of what degree and in which direction?

• The first question is answered by the use of correlation technique and the second by regression technique.
• Karl Pearson's coefficient of correlation (or simple correlation) is the most widely used method of measuring the degree of relationship between two variables. The value of 'r' lies between +1 and -1 showing the perfect positive correlation and perfect negative correlation respectively.

Statistical Tests

While analysing quantitative data a number of tests can be used.

• When population is normal or sample size is large (i.e. n>30) or population variance is known then we have to use z-test.


• When population is normal and sample size is small (i.e. n<30)>
  
• When we want to test the equality of variance of two normal populations, we make use of F-test based on F-distribution

By comparing the observed value of F with the corresponding table value,we can infer whether the difference between the variance of samples could have arisen due to sampling fluctuation.

If the calculated value of F is greater

नेपालीमा पनी लेखन गर्न सकिन्छ

नेकपा एमाले सरकारमा जान लागेको छ। तर एसको प्रभाव राम्रो होला जस्तो मलाई लाग्दैन। माधव कुमार नेपाल प्रधान मंत्री त होलन तर नेपालको बिकास हुन भने सक्दैन।

Hypothesis Testing

Hypothesis Testing
Hypothesis
In a quantitative रिसर्च we have to formulate hypotheses and test them. A hypothesis is a proposition or a set of propositions set forth as an explanation for the occurrence of some specified group of phenomena either asserted merely as a provisional conjecture to guide some investigation or accepted as highly probable in the light of established facts (Kothari).
Types of Hypotheses
a. Null hypothesis (Ho)
Ho = Development Activists are positive to validation.
b. Alternative hypothesis (Ha)
Ha = DA are not positive to validation
- If sample results do not support null hypothesis, we should conclude that something else is also true. What we conclude rejecting the null hypothesis is known as alternative hypothesis.
- Alternative hypothesis is usually the one which one wishes to prove. And the null hypothesis is the one which one wishes to disprove.
For example:
- Ho: Educational Stakeholders are negative to validation
- Ha: Educational Stakeholders are positive to validation.
The level of significance
- It is always some percentage (usually 5%) which should be chosen with great care, thought and reason. In case we take the significance level at five percent, then this implies that Ho will be rejected when sampling result has a less than 0.05 probability of occurring.
- The five percent level of significance means that researcher is willing to take as much as 5 percent risk of rejecting the Ho when it happens to be true.
Hypotheses of my research

Ho: Educational stakeholders perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
Ha: Educational stakeholders perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
Theme wise hypotheses
a. Theme I: Providing options for learning (OFL)
Ho: ES have negative attitude towards providing different options (formal, non-formal and informal) for learning to learners.
Ha: ES have positive attitude towards providing different options (formal, non-formal and informal) for learning to learners.
b. Theme II: Establishing parity of esteem (POE)
Ho: ES have negative attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
Ha: ES have positive attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
c. Theme III: Developing a national qualifications framework (NQF)
Ho: ES have negative attitude towards developing a national qualifications framework
Ha: ES have positive attitude towards developing a national qualifications framework.
Respondent wise hypotheses
a. Development Activists
Ho: DA perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
Ha: DA perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
b. Educational Administrators
Ho: Educational Administrators perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
Ha: Educational Administrators perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
c. Policy Actors
Ho: Policy Actors perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
Ha: Policy Actors perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
d. University Professor
Ho: University Professor perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
Ha: University Professor perceive the possibility of identifying, recognizing and validating non-formal and informal learning to open up avenues for lifelong and continuing education in Nepal negatively.
Respondent and theme wise hypotheses
1. DA with OFL
Ho: DA have negative attitude towards providing different options (formal, non-formal and informal) for learning to learners.
Ha: DA have positive attitude towards providing different options (formal, non-formal and informal) for learning to learners.
2. DA with POE
Ho: DA have negative attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
Ha: DA have positive attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
3. DA with NQF
Ho: DA have negative attitude towards developing a national qualifications framework
Ha: DA have positive attitude towards developing a national qualifications framework.
4. EA with OFL
Ho: EA have negative attitude towards providing different options (formal, non-formal and informal) for learning to learners.
Ha: EA have positive attitude towards providing different options (formal, non-formal and informal) for learning to learners.
5. EA with POE
Ho: EA have negative attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
Ha: EA have positive attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
6. EA with NQF
Ho: EA have negative attitude towards developing a national qualifications framework
Ha: EA have positive attitude towards developing a national qualifications framework.
7. PA with OFL
Ho: PA have negative attitude towards providing different options (formal, non-formal and informal) for learning to learners.
Ha: PA have positive attitude towards providing different options (formal, non-formal and informal) for learning to learners.
8. PA with POE
Ho: PA have negative attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
Ha: PA have positive attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
9. PA with NQF
Ho: DA have negative attitude towards developing a national qualifications framework
Ha: DA have positive attitude towards developing a national qualifications framework.
10. UP with OFL
Ho: UP have negative attitude towards providing different options (formal, non-formal and informal) for learning to learners.
Ha: UP have positive attitude towards providing different options (formal, non-formal and informal) for learning to learners.
11. UP with POE
Ho: UP have negative attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
Ha: UP have positive attitude towards establishing parity among three forms of learning (formal, non-formal and informal).
12. UP with NQF
Ho: DA have negative attitude towards developing a national qualifications framework
Ha: DA have positive attitude towards developing a national qualifications framework.
Comparison among the type of respondents
Ho: There is a significant difference among the opinion of DA, EA, PA and UP regarding validation.
Ha: There is a no significant difference among the opinion of DA, EA, PA and UP regarding validation.
Comparison among the type of respondents regarding themes
a. Theme I: Providing options for learning
Ho: There is a significant difference among the opinion of DA, EA, PA and UP regarding OFL.
Ha: There is a no significant difference among the opinion of DA, EA, PA and UP regarding OFL.
b. Theme I: Establishing parity of esteem
Ho: There is a significant difference among the opinion of DA, EA, PA and UP regarding POE.
Ha: There is a no significant difference among the opinion of DA, EA, PA and UP regarding POE.
c. Theme I: Developing a national qualifications framework
Ho: There is a significant difference among the opinion of DA, EA, PA and UP regarding NQF.
Ha: There is a no significant difference among the opinion of DA, EA, PA and UP regarding NQF.
Test of Hypotheses
There are several tests of hypotheses (also known as the test of significance) for the purpose of testing hypotheses. They can be classified as:
a. Parametric tests or standard tests of hypotheses
b. Non-parametric tests or distribution-free tests of hypotheses
- Parametric tests usually assume certain properties of the present population from which we draw samples. Assumptions like observations come from a normal population, sample size is large, and assumptions about the population parameters like mean, variance, etc. must hold good before parametric test can be used.
- But there are situations when the researcher can’t or doesn’t want to make such assumptions. In such situations we use statistical methods for testing hypotheses which are called non-parametric tests because such tests do not depend on any assumptions about the parameters of the parent population.
While analyzing quantitative data a number of tests can be used:
When population is normal or sample size is large (i.e. n>30) or population variance is known then we have to use z-test.
When population is normal and sample size is small (i.e. n<30) and population variance is unknown then we have to use t-test.
When we want to test the equality of variance of two normal populations, we make use of F-test based on F-distribution
One-way ANOVA is used to test for differences among two or more independent groups.
By comparing the observed value of F with the corresponding table value, we can infer whether the difference between the variance of samples could have arisen due to sampling fluctuation.
If the calculated value of F is greater than table value of F at certain level of significance and degree of freedom, we regard the F-ratio as significant. On the other hand if the calculated value of F is smaller than its table value, we conclude that F-ratio is not significant. If F-ratio is considered not significant we accept the null hypothesis; but if F-ratio is considered significant we then reject the null hypothesis or accept the alternative hypothesis.

Back to the Web World Again

I was out of contact from the world of Internet for more than two months. One of the reasons was that the Internet Service provided by Websurfer was stopped. Now I have taken Internet service from Nepal Telecom. Though it was difficult to manage telephone line and to take ADSL service, finally I am now connected. It took me nearly 1 month to have this facility.
Another reason was that I was busy in writing books for school level. Inclusive Social Studies Book Introductory to Book 10 (11 books altogether) published this year.
The third reason was that I went to Kapilvastu for a research related School Sector Reform Plan, from the Ministry of Education. It took nearly one and half month for field study and report preparation.
Now, I am complelty devoted to finish my thesis.