Statistics in Research. 2020.ppt

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Dr. Santiago & Dr. Rosa Padilla de

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QUALITATIVE RESEARCH



Dr. Santiago & Dr. Rosa Padilla de Casamayor

Qua litati ve rese arch see ks to tell the sto ry o

f a p_arti

cula_r gro up's exp erie_nce s in the ir ow n w ord s, an d is the refo re fo cuse d on narr_ativ e (w hile qua ntita tive rese

arch_fo cuse

s on num

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How Much Time Do Young Rwandese Spend on

Their Mobile Phones in 2020?

What were they doing when they use their phones?

Entertainment, academically researching, to shop…

How much money do students spend to use their

phones?

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Dr. Santiago & Dr. Rosa Padilla de Casamayor 4

Research

methodolog

y

Title (variables) / Problem definition / Research objectives / Research hypothesis

•Direct observation •Survey/questionnaires •Experiments

•Existing databases

• Validity: are you measuring what you think you are measuring?

• Reliability: if something was measured again using the same instrument, would it produce the same (or nearly the same) results?

The objective of

classification of data is to make the data simple, concise, meaningful and interesting and helpful in further analysis

Research approach: •Quantitative

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Role of Statistics in Research



 Designing research

 Analyzing data

 Draw conclusion about research.

Initial questions: • Is it feasible to collect the data?

• Evaluate the feasibility of the study objectives; that is, evaluate if it is measurable what you want to measure.

• What analysis will you use in your research?

Fit the statistics to the objectives, research question and research hypothesis; and also according to the type of variables are you studying.

Identified variables needed to achieve the objective (s)

 Are you interested in…

Describing a sample or outcome

Looking at how groups differ

Looking at how outcomes are related

Looking at changes over time

Creating a new scale or instrument

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Areas of Statistics

 Descriptive Statistics (do not test any hypothesis)

o It Concern with development of certain indices from the raw data

oIt summarizes collected/classified data

oMeasure of central tendency, measure of variability or dispersion, measure of asymmetry & measure of position)

oMeasure of relationship

oOthers measures (index number, time series analysis, etc)

 Inferential Statistics

o Is a set of methods used to make generalization, estimate, prediction or decision

o It adopts the process of generalization from small groups to population (using sampling statistics)

o Have two major problems

 Estimation of population parameters

 Testing of statistical hypothesis

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Dr. Santiago & Dr. Rosa Padilla de Casamayor What is the impact of X on Y?

To what is the extent X affect Y? What are factors that affect …?

What are critical sources factors?

Research question Research Methodology Paradigm What? Why? How? Survey Case study Grounded theory Action research Positive paradigm: Hypothesis testing Interpretative paradigm:

It is concerned with understanding the

world as it is from subjective expe-riences of individuals.

Grounded theory is

mainly used for qualitative research (Glaser, 2001), it is a general method of analysis that accepts qualitative, quantitative, and hybrid data collection from surveys,

experiments, and case studies (Glaser, 1978).

Action research can be defined as

“an approach in which the action researcher and a client collaborate in the diagnosis of the

problem and in the

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Association Test according the objective and the type of variable

8 Dr. Santiago & Dr. Rosa Padilla de Casamayor

Test of Association

Dependent (outcome) Variable Independent (explanatory) variable Parametric test (data is

normally distributed)

Non-parametric test (ordinal/ skewed

data

Relationship between 2

continuous variables Scale Scale

Simple Pearson's Correlation Coefficient Spearman's Correlation Coefficient Predicting the value of one

variable from the value of a predictor variable or looking

for significant relationships Scale Any

Simple Linear or non-linear

Regression Transform the data

Predicting the value of one variable from the value of a

predictors variable or looking for significant

relationships Scale Any (more than one variable) Multiple Linear or non-linear Regression Nominal (Binary) Any Logistic regression Assessing the relationship

between two or more

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Association Test according the objective and the type of variable

Partial correlation



In simple correlation, we measure the strength of the linear

relationship between two variables, without taking into consideration the

fact that both these variables maybe influenced by a third variable.

Example:



Correlation between price and demand, we completely ignore the

effect of other factors like:



Money supply



Import and export, etc

Of course those variables definitely have a bearing on the price

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Comparison Test according the objective and the type of variable

10 Dr. Rosa Padilla de Casamayor

Comparison

Test

Dependent

(outcome)

Variable

Independent

(explanatory)

variable

Parametric

test (data is

normally

distributed)

Non-parametric test

(ordinal/ skewed data)

or 'assumption not

assumed'

The average score of

two independent groups

Scale

Nominal

(binary)

Independent

t-test

Mann-Whitney

test/wilcoxon rank

sum

The average of three 3+

independent groups

Scale

Nominal

One-way

ANOVA

Kruskal-Wallis test

The average difference

between paired

(matched) samples

'before and after'

Scale

Time/

condition

variable

Paired t-test

Wilcoxon signed rank

test/ Mc Nemar

The 3+ measurements

on the same subject

Scale

Time/

condition

variable

Repeated

measures

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t

-Test for Comparing Two Means

Example

: Researchers are

interested in test anxiety. They

administered an inventory of

anxiety to the students just

before the final exam in a

Sociology class. They also

administered it before the

final exam in a business class.

To compare the two sets of

scores, they use

t-test for independent samples

Example

: Researchers are

interested in exam anxiety.

They administer an anxiety

inventory on the second day of

class. Then they give it again on

the day of the midterm. To

compare the two sets of

scores,

they use

t-test for paired samples

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Anxiety test score

Student

Second day of class

Midterm

1 67 89 2 45 55 3 75 70 … …

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

n way ANOVA: comparing two or more separate independent

variables on one dependent variable (e.g. Three teachers

taught statistics course , and which teaching method was

used (online, face to face with calculator, or with software) –

Average post-test assessment score.



Mixed ANOVA: Used when comparing more than one group

over more than one-time-point on a measure (e.g. Females Vs

Males students, before and after a foreign language

course-Average score on an assessment)



Analysis of covariance (ANCOVA): examining the differences

among groups while controlling for an additional variable

(e.g. online or face to face course, controlling for baseline

knowledge – average post-test assessment score)

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

Analysis of dependence

Where one (or more) variables are dependent

variables, to be explained or predicted by others

E.g. Multiple regression, Partial least squares path

analysis, Multiple discriminant analysis



Analysis of interdependence

- No variables thought of as ‘dependent’

- Look at the relationships among variables, objects or

cases

E.g. Cluster analysis, factor analysis

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Dr. Santiago & Dr. Rosa Padilla de Casamayor 14

One or more

None

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Medicine

– Does a drug work? Does the average life expectancy

significantly differ between the three groups that received the

drug versus the established product versus the control?

Sociology

– Are rich people happier? Do different income classes

report a significantly different satisfaction with life?

Management Studies

– What makes a company more

profitable? A one, three or five-year strategy cycle?

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Independent variable

Metric Non-metric

Dependent variable

Metric Regression ANOVA

Non-metric Discriminant analysis

Chi square

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Purpose of hypothesis testing

• The purpose of hypothesis testing is to determine whether there is

enough statistical evidence in favor of a certain belief about a

parameter.

• A hypothesis may be precisely defined as a tentative proposition

suggested as a solution to a problem or as an explanation of some

phenomenon. (Ary, Jacobs and Razavieh, 1984)

Example

:

“There is no significant

difference in the anxiety level of

children of High IQ and those of

low IQ.”

Achievement and Enrollment Status of Suspended Students

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The critical concepts are these:

1. There are two hypotheses: the null and the alternative hypotheses.

2. The procedure begins with the assumption that the null hypothesis is

true.

3. The goal is to determine whether there is enough evidence to infer

that the alternative hypothesis is true, or the null is not likely to be

true.

Statistical Hypothesis Testing

4. There are two possible decisions:

Reject the null hyphotesis: To

conclude that there is enough

evidence to infer that the

alternative hypothesis is true.

Fail to reject the null hypothesis:

To conclude that there is

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An alternative hypothesis is a statement that suggests a potential

outcome that the researcher may expect. (H1 or Ha)

• Comes from prior literature or studies.

• It is established only when a null hypothesis is rejected.

• Often an alternative Hypothesis is the desired conclusion of the

researcher.

• The two types of alternative hypothesis are: Directional Hypothesis

Non-directional Hypothesis.

Alternative Hypothesis (Ha)

Directional: Is a type of alternative hypothesis that specifies the direction of expected findings. Sometimes directional hypothesis are created to examine the relationship among variables rather than to compare groups. Directional hypothesis may read,”…is more than..”, “…will be lesser..”

Example: “Children with high IQ will exhibit more anxiety than children with low IQ”

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Statement:

the mean life expectancy in Rwanda, 2019

is 69.02 years

Source:https://knoema.com/atlas/Rwanda/topics/Demographics/ Age/Life-expectancy-at-birth

is 60: x = 60 years

If X=60 likely if Ho:



= 69.02

REJECT

Null Hypothesis

If not likely,

Hypothesis Testing Process

Suppose the

sample mean of the Life expectancy H0:  = 69.02

Ha:  ≠ 69.02

Sample

Population

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To make a decision we need to interpret Sig. or P_value

The smaller Sig or p-value, the more statistical evidence exists to support the

alternative hypothesis.

•If Sig.

is

less than 1%,

there is

overwhelming evidence

that supports the

•If Sig.

is

between 1% and 5%,

there is a

strong evidence

that supports the

•If Sig.

is

between 5% and 10%

there is a

weak evidence

that supports the

•If Sig.

exceeds 10%,

there is

no evidence

that supports the alternative

hypothesis.

Overwhelming

Evidence

(Highly

Significant)

Strong Evidence

(Significant)

Weak Evidence

(Not Significant)

No Evidence

(Not Significant)

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Actual

situation

Our

decision

Null (Ho)

hypothesis is

false

Null (Ho)

hypothesis is

true

Reject the null

(Ho) hypothesis

Correct

decision

Type I

error (α)

Called Level of Significance

Do not reject the

null (Ho)

hypothesis

Type II

error (β)

Correct

decision

(1-β)

Types of Errors

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Procedures for sample size calculation

25 Dr. Santiago & Dr. Rosa Padilla de

Casamayor

• Selection of primary variables of interest

• Information of standard deviation ( if numeric) or

proportion (if categorical)

• a specified margin of error (precision) that the

investigator specifies

•

Z

is the value from the table of probabilities of the

standard normal distribution for the desired

confidence level (e.g., Z = 1.96 for 95% confidence)

• Selection of reasonable test statistic

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Thanks

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Principles in tabulation of data

Casamayor

1. Every table should contain a title, should be concise and

meaningful.

2. The tables should be numbered .

3. The heading of columns or rows should be clear and

concise. e.g.: height in cm, age in years, weight in kg.

etc.

4. The number of class intervals should be sufficient to

condense the data bringing out their significant features.

5. Uniform size class intervals are preferable.

6. Units of measurements should be specified.

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Website course

•

https://sites.google.com/a/upeu.edu.pe/rosa-padilla/

Dr. Santiago & Dr. Rosa Padilla de

t-test for independent samples

t-test for paired samples

https://sites.google.com/a/upeu.edu.pe/rosa-padilla/