Question:
Describe about the main ideas of quantitative methods?
Literature review and ANOVA
In a today’s, the qualitative and quantitative research is become so much important. The process of doing both qualitative and quantitative research at a time is called as mixed research models. There are so many skills required for doing this analysis for mixed research models. First we have to decide our goal or aim for the research. After deciding this aim, then we need to categorize the data collected by using the instrument. Data collection is very important step in the research process. If there is mistake during the process of collecting data, it results into wrong estimates about the population. Taking care during collecting data is very important factor in the research process. After collection of this data, we need to classify whether this data is qualitative or quantitative. Then after, the data analysis is the important part for proving our claims. In data analysis, we use different statistical methods. There may be different statistical methods for the quantitative and qualitative data. Also sometimes it is depends upon what we have to prove. After data analysis, the last task is to write the results or conclusions for our study.
In quantitative data analysis, there are two main categories of data analysis. First is descriptive statistics and second is the inferential statistics. In the descriptive statistics analysis, we study the variables for the mean, mode, median, minimum, maximum, range, standard deviation, variance, kurtosis, skewness, etc. That is, we study all the descriptive measurements regarding the variables in this descriptive analysis. Descriptive analysis of the variable gives us the idea about the data regarding the variable under study. Range and standard deviation provides view about the spread of the data and skewness provides the skew of the data. In fact we understand the what type of the distribution of the data for the given variable is. Study of descriptive statistics for each variable under study is very important because it gives us some clue for the next inferential statistics. It also provides the facility of comparison between the different descriptive statistics among the different variables under study.
Inferential statistics is the main part for the data analysis. It provides us the testing of hypothesis for the different claims regarding the variables or data under study. In the testing of hypothesis, we establish the null and alternative hypothesis or we can say that we test the claim of researcher. Then we decide the some level of significance or alpha value for this test. Most of the time, we take a level of significance as the 5% or 0.05. Next step in the testing of hypothesis is the finding the test statistic value. We use the test statistic formula for the calculation of the test statistic value. Selection of the proper test for the claim is very important in the testing of hypothesis. There are several statistical hypothesis tests are available and proper selection is depends upon what we want to prove. After finding out the test statistic value, we can find the p-value for this test. After finding the p-value we compare this p-value with the alpha value or given level of significance for this hypothesis test. Then at last we take the decision about the null hypothesis or the claim associated with this test. We reject the null hypothesis if the p-value is less than the given level of significance and we do not reject the null hypothesis if the p-value is greater than the given level of significance or alpha value.
Now, we have to see for what purpose we use the ANOVA. ANOVA is nothing but the analysis of variances. It is used when there are more than two variables. When we have only two samples, then we can use t test or z test but there are so many situations, there are more than two variables are available for analysis. In this situation we need to use the ANOVA test. ANOVA found very important in the analysis of the multiple variables. One way ANOVA is the statistical technique for testing the equality of the population means for three or more than three variables. In this test, there are so many calculations but due to the availability of different software, it gives us fast result. We uses ANOVA test for checking whether all the population means are same or not. In other words, we check whether a difference in all treatments and among treatments is. We take the decision about ANOVA based on p-value. We know the decision rule for rejecting or not rejecting null hypothesis. The decision rule is given as below:
Decision rule: We reject the null hypothesis when the p-value is less than the given level of significance or alpha value. We do not reject the null hypothesis when p-value is greater than the given level of significance or alpha value.
So, we take the decision according to the decision rule given above and then at final, we write the conclusion about the null hypothesis for study.
In this topic, we have to see the different test of independence. First we have to see the chi square test for independence.
Here, we have to see how we have to conduct the chi square test for independence. We use this test when we are given the two categorical variables from the single population. By using this test, we have to check whether there are any significant association exists between these two variables or not. There are so many examples for categorical data. For example, in surveys voters are divided as male and female. This chi square test for independence has mainly four steps given as below:
The null and alternative hypotheses are given as below:
Null hypothesis: Variables under study are independent.
Alternative hypothesis: Variables under study are not independent.
Next step in this test is to decide the level of significance. It is important because it gives us the margin of accuracy of results. After deciding level of significance or alpha value, we need to find out the test statistic value. After finding test statistic value, we find the p-value. Then we take the decision about null hypothesis based on the p-value. Last step is to make a conclusion about the null hypothesis.
5 journal articles
Article 1:
In this article, researcher study the different variables regarding the education, occupation and earnings. Researcher also find out the relationship between the education and occupation, education and earning; and occupation and earnings. Also researcher find the collectively relationship among the three variables education, occupation and earnings. Researcher uses different statistical analysis for this study. First of all researcher collects the data for the education, occupation and earnings. Then he arranges this data in a systematic format for next study. Then after he divide this data according to the different category such as male and female, etc. dividing data is very important because this would helpful for the analysis of particular category. Then researcher find out the some descriptive statistics for these variables under study. The study of descriptive statistics is very important because it gives the brief idea about the data under study. After this researcher find out the correlation coefficients between the different pairs of variables. Researcher finds the correlation coefficients between the variables education and occupation, education and earnings and finally he find out the correlation coefficient between the occupation and earnings. Also researcher find out the correlation coefficients according to the gender of the person involved in this study. Then researcher uses the different design of experiments for this study. The model of multiple regression is used for the study of relationship between the three variables education, occupation and earnings. After some calculations, researcher find out the multiple regression equation for the relationship between the education, occupation and earnings. Researcher test the claim that there is significant relationship exists between these three variables. Researcher found that there is significant linear relationship exists between these three variables under study.
Then after, researcher added some more variables for this study. Researcher added the variable like achievements in early career, etc. Then again find out the relationship between the different pairs and find out the results and regression equations for the different pairs.
Inequality among world citizens: 1820 – 1992
This article investigates the distribution of well being among world citizens during the last two centuries. The results of this study show the inequality of world distribution for the income during the period of 19th century. This article studies some theoretical issues about the world distribution of income. The study was focused on international differences in GDP per capita. This article shows that inequality among the countries is the key factor in world inequality. But, this article also shows that world inequality is not well approximated by testing hypothesis that all civilians in the same country have same income.
For this purpose, they used different tests and other statistical methods. For different hypothesis they used different suitable tests of hypothesis and then according to the p-value they take the decisions about null hypothesis.
For the study of above discussed article, they collected the data from each country and then use this data for analysis. One sample tests, two sample tests and multiple sample tests were used for this study of inequality among world citizens.
There was a rich history for the study of reading comprehension research. There are so many different issues regarding the reading comprehension. This article also explains the idea of teaching comprehension. In this article, the things by good readers are given as below:
Good readers are active readers.
From the outset they have clear goals in mind for their reading. They constantly evaluate whether the text is meeting their goal or not.
A good reader looks over the text or book before they read.
There are so much reasons or activities described for the good readers. For the study of different hypothesis regarding the reading comprehension, data is collected for the two different groups. With practice and without practice data collected for testing the hypothesis regarding the reading comprehension. Then by using this data, they perform the appropriate test and at finally take the decision about null hypothesis whether it have to reject or do not reject. We take this decision by comparing the p-value and level of significance or alpha value. We know that if the p-value is less than the level of significance or alpha value, then we reject the null hypothesis and if the p-value is greater than the level of significance or alpha value, then we do not reject the null hypothesis.
For this article, researcher collects the self reported data for the men and women from the year 1973 to 1974. Here researcher collects the self reported data first and then again collects the actual real data for the height and weight for the men and women. Then researcher arranges this data in a systematic format according to the two categories such as male and female. After doing this, researcher calculate the different proportions for the height and weight of the male and female respondents. Researcher uses some tests for checking his claims. After doing all these, researcher draws some conclusions regarding the data of height and weight for the male and females. Researcher wants to check the accuracy of this data. The recorded data is regarding with the height and weight of the men and women. Researcher found that men and women both were reported, on the average, with small but systematic errors. Researcher found that larger errors were obtained in certain population subgroups. Also researcher found that men and women differed somewhat in the pattern of misreporting. Researcher found that weight was understated by 1.6% by men and 3.1% by women while height was overstated by 1.3% by men and 0.6% by women.
Researcher found in the previous studies that the most important correlates of the amount of error were actual measurements of height and weight. Researcher found the interesting finding that misreporting of both height and weight in men was correlated with both aspects of body size, whereas for women, it was related mainly to the characteristic in question. Researcher also found the impact of the some demographic variables such as age and educational level has some importance in the misreporting of the height and weight.
Here, researcher uses the method of instrumental variables. This method was first used in the 1920s for estimation of the supply and demand elasticity’s. Again this method was used to correct the measurement error in the single equation models. Currently instrumental variables are widely used for the reduction of the bias from the omitted variables in the estimation of the causal relationships such as the effect of schooling on earnings. Here researcher use the method of randomized experiments for the study of supply and demand. Also researcher study the pattern for the supply and demand.
Researcher also conclude that an instrumental variables estimate of the demand elasticity can be constructed by dividing the sample covariance between the log quantity of flaxseed and the yield per acre by the sample covariance between the log price of flaxseed and the yield per acre. This estimate is consistent estimate. This is consistent as long as the yield per acre is uncorrelated with the error in the demand equation and correlated with price. Researcher also found that replacing the yield per acre by the price of substitutes for this calculation, then it generates an instrumental variables estimate of the supply elasticity.
References:
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