Data Analysis and Hypothesis Testing           

Data analysis is defined as a process of cleaning, transforming and modeling data to discover useful information for business decision making. The purpose of data analysis is to extract useful information from data and taking the decision based upon the data analysis.

Data analysis is the process of evaluating data using the logical and analytical reasoning to carefully examine each component of the data collected or provided. Also is one of the many step that are, taken when a research experiment is conducted.

Many types of Data Analysis (Method)                                                

1. Qualitative Data Analysis

                 Descriptive Analysis.

                Predictive Analysis.

                Prescriptive Analysés.

               Content Analysis.

               Narrative Analysis.

              Grounded Analysis.

             Converation Analysis.

             Discourse Analysis.

2. Quantitative Data Analysis

                   Mean

                   Mode

                   Standard diriation

                   Regrassion

                  Hypothesis testing

                 Sample size Determination.

                Percentage

               Frequency

1. Qualitative Data Analysis                                                                                                

The data obtained through this method consists of words, picture, symbols, and observation and interview. This type of analysis refers to the procedures and processes that are utilized for, the analysis of data to provide some level of understanding, explanation or interpretation.

Descriptive Analysis

(know of present)

Predictive Analysis

(know of future)

Prescriptive Analystics

Content Analysis

It is used to analyze verbal or behavioral data. This data can consist of documents or communication artifacts like texts in various formats, picture or audio / videos.

Narrative Analysis

This one is the most commonly used as it involves analyzing data that comes from a variety of sources including field notes, survey, diaries, interviews and other written froms. It involves reformulating the stories given by people based on their experiences and in different contexts.

Grounded theory

This method involves the development of causal explanations of a single phenomenon from the study of one or more cases. If further cases are studies, them the explanations are altered until the researchers arrive at a statement that fits all of the cases.

2. Quantitative Data Analyses                                                                                             

As the name suggests, the quantitative analysis is used for the quantitative of data which allows the generalization of the results obtained from a sample to a population of interest.

Simply put, statistical methods of data analysis are used to collect raw data and transform it into numerical data some of the methods that fall under that quantitative analysis are :

Mean

Also known as the average, mean is the most basic method of analysing data where the sum of a numbers list is divided by the number of items on that list. It is useful in determining the overall trend of something

Hypothesis testing

Majorly used in business research and is done to assess if a certain theory or hypothesis for a population or data set is true.

Sample Size Determination

When doing research on a lange population like workforce for your company, small sample size is taken and then analyzed and the results are considered almost some for every member of the population.

 Hypothesis Testing                                                                               

The Hypothesis is an assumption which is tasted to check whether the inference drown from the sample of data stand true for the entire population or not.

Hypothesis testing refers to :

i. Making an assumption, called hypothesis, about a population parameter.

ii. Collecting sample data.

ii. Calculating a sample statistic.

iv. Using the sample statistic to evaluate the hypothesis (how likely is it that our hypothesized parameter in correct. To test the validity of our assumption we determine. the difference between the hypothesized parameter value and the sample value)

Process of Hypothesis testing                                                               

Level of significance and power of test

The factors that affect the level of significance are :

a. The magnitude of the difference between sample means;

b. The size of the samples;

c. The variability of measurements within samples; and

d. Whether the hypothesis is directional or non-directional.

(A directional hypothesis is one which predicts the direction of the difference between, say, means)

1. Making a formal statement

The step consists in making a formal statement of the null hypothesis (Ho) and also of the alternative hypothesis (Ha)

This means that hypothesis should be clearly stated, considering the nature of the research problem. Null hypothesis No difference.

Example -

Mr. Mohan of the civil engineering Department wants to test the load bearing capacity of an old bridge which must be more than 10 tons, in that care the can state his Hypothesis as under :

Null hypothesis (Ho) : Tons μ = 10

Alternative hypothesis (Ha) : Tons μ >10

2. Selecting a significance level

The hypothesis are tested on a pre-determined level of significance and as such the same should be specified. Generally, in practice, either 5% level or 1% level is adopted for the purpose.

A- P-value less than 0.05 (typicall ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.

3. Deciding the distribution to use

After deciding the level of significance, the next step in hypothesis testing is do determine the appropriate sampling distribution.

4. Selecting a random sample and computing an appropriate value

Another step is to select a random sample(s) and compute an appropriate value from the sample data concerning the test statistic utilizing the relevant distribution. In other words, draw a sample to furnish empirical data.

5. Calculation of the probability

One has then to calculate the probability that the sample result would diverge as it has from expectations, if the null hypothesis were infact true.

6. Comparing the probability

Yet another step consists in comparing the probability thus calculated with the specified value for a, the significance level.

If the calculated probability in equal to or smaller than the a value in case of one-tailed test (and a/2 in case of two-tailed test), then reject the null hypothesis (i.e. - accept the alternative hyp thesis), but if the calculated probability is grather then accept the null hypothesis.

 Hypothesis test two type                                                                       

i. One tailed

ii. Two tailed

Normal Distribution

In statistics the theoretical curve that shows how often an experiment will produce a particular result.

The curve is bell shaped, sho-wing that trials will usually give a result near the average, but will occasionally deviate by large amounts.

Normal distributions are symmetric, unimodal, and asymptotic and the mean median, and mode are all equal.

For example, if flipping a coin, testing whether it is biased towards heads and getting data of 'all heads' would be seen as highly significant, white getting data of 'all tails' would be not significant at all (P=1)

By contrast, testing whether it is biased in either direction i.e. either 'all heads' or 'all tails' would both be seen as highly significant data.

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One-Tailed Test

A one-tailed test is a statistical test in which the critical area of a distribution is one-sided so that it is either greater then or less than a certain value, but not both.

If the sample being tested falls into the one sided critical area, the alternative hypothesis will be accepted instead of the null hypothesis.

picture

Two-Tailed test

Two-tailed hypothesis tests are also known as non-directional and two-sided tests because you can test for effects in both directions.

When you perform a two-tailed test, you split the significance level percentage between both tails of the distribution.

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Error

A hypothesis is an assumption that may prove to be either correct or incorrect.

It is possible to arrive at an incorrect conclusion about a hypothesis for a variety of reasons.

Incorrect conclusions about the validity of hypothesis may be drawn it.

The study design selected in faulty.

The sampling procedure adopted is faulty.

The method of data collection is inaccurate.

The analysis in wrong.

The statistical procedures applied are inappropriate; or

The conclusion drawing are incorrect.

Hence, in drawing conclusions about a hypothesis, two types of error can accur ;

Rejection of a null hypothesis when it is true. This is known as a Type 1 error.

Alfa Error

Faild Researcher ( Big Error)

Acceptance of a null hypothesis when it is false. This is known as a Type 2 error.

Bita Error

Faild Sample size / Population size (Small error)

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 Hypothesis statistical tests                                                                   

a. Z-test (above-30) / Large simple size ( Population known)

b. T-test (Less-30) / Small population ( Population Unknown)

c. Chi-square test

d. F-test

e. Analysis of variance (ANOVA)

a. Z-test (Compare two independent sample)

Z-test refers to a univariate statistical analysis used to test the hypothesis that proportions from two independent samples differ greatly. It determines to what extent a data point is away from its mean of the data set, in standard deviation.

The researcher adopts z-test, when the population variance is known, in essence, when there is a large simple size (above 30), simple variance is deemed to be approximately equal to the population variance. In this way, it is assumed to be known, despite the fact that only sample data is available and so normal test can be applied.

Large population (above 30)

Stand division known

Variance known

Normal distribution (Ratio study)

All sample observations are independent

Mean zero and variance 1

Where two population means are different

b. T-test W. Gossel 1908

The T- test can be understood as a statistical test which is used compare and analyse whether the means of the two population is different from one another on not when the standard deviation is known.

Population variance is unknown.

Small population (less then 30)

Standard deviation is not known

c. Chi-square test Goodness fit test

The chi-square test is a statistical procedure used by researchers to examine the differences between categorical variables in the same population.

The Chi-square test informs researchers about whether or not there is a statistically significant difference between how the various segments or categories answered a given question non-parameter answer to yes or no.

To check the compatibility of observed and expected frequency.

d. F-fest / significant of regration test

F-test for testing equality of variances of two normal population. The F Distribution is named after R.A. Fisher used to medical.

Sample have been drawn randomly

Observation are Independent

There is no measurement error

Ha may be one side or two tail

Notes : 

Question : 

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