Cronbach Alpha

➢Cronbach’s alpha or coefficient alpha, denotedby α and developed by Lee Cronbach in 1951, is ameasure of internal consistency, that is, how closelyrelated a set of items are as a group.

➢For example, a company might give a jobsatisfaction survey to their employees. High reliabilitymeans it measures job satisfaction, while lowreliability means it measures something else (orpossibly nothing at all).

Lee Cronbach

➢A high value of alpha indicates that the instrumentis reliable.

➢ A high level for alpha may mean that the items inthe test are highly correlated.

Cronbach Alpha

➢A low value of alpha indicates that the instrumentis not reliable.

➢ A low level for alpha may mean that the items inthe test have low correlation.

➢Theoretically, Cronbach’s alpha results shouldgive you a number from 0 to 1, but you can getnegative numbers as well.

Cronbach Alpha

➢A negative number indicates that something is wrongwith your data – perhaps you forgot to reverse scoresome items or your data input is incorrect.

➢The general rule of thumb is that a Cronbach’s alpha of .70 and above isgood, .80 and above is better, and .90 and above is best.

Cronbach Alpha

➢Cronbach’s alpha does come with some limitations:

➢ scores that have a low number of items associated with them tend to havelower reliability, and

➢sample size can also influence your results for better or worse.

➢ a “high” value for alpha does not imply that the measure is unidimensional.

Cronbach Alpha

➢Uni-dimensionality in Cronbach’s alpha assumes the questions areonly measuring one latent variable or dimension. If you measure morethan one dimension (either knowingly or unknowingly), the test resultmay be meaningless.

• Click“Analyze,”then click“Scale” andthen click“ReliabilityAnalysis.”

Step 1

• Transfer yourvariables (q1to qn) into“Items,”. Themodel defaultshould be setas “Alpha.”

Step 2• Click

“Statistics” inthe dialogbox.

Step 3

• Select “Item,” “Scale,” and “Scale if item deleted” in the box description. Choose “Correlation” in the inter-item box.

Step 4

• Click“Continue”and then click“OK”.

Step 5

Cronbach Alpha in SPSS

Parametric Test

Statistical Tests

➢A parametric test is a hypothesis testing procedure based on the assumption

that observed data are distributed according to some distributions of well-

known form (e.g., normal, Bernoulli, and so on) up to some unknown

parameter(s) on which we want to make inference (say the mean, or the

success probability).

➢Parametric tests assume a normal distribution of values, or a “bell-shaped

curve.” They are in general more powerful (require a smaller sample size)

than nonparametric tests.

Non-Parametric Test

Statistical Tests

➢A non-parametric test (sometimes called a distribution free test) does not

assume anything about the underlying distribution (for example, that the data

comes from a normal distribution).

➢Most nonparametric tests use some way of ranking the measurements and

testing for weirdness of the distribution.

Non-Parametric Test

Statistical Tests

Non-parametric tests are often necessary. Some common situations for

using nonparametric tests are:

➢ when the distribution is not normal (the distribution is skewed),

➢the distribution is not known, or the sample size is too small (<30) to assume a

normal distribution,

➢if there are extreme values or values that are clearly “out of range,” nonparametric

tests should be used.

Statistical Tests

Statistics That is Descriptive in Nature

Statistical Test Test Statistic Purpose

Frequency fis used when you want to show how often a response is given

(counting, frequency, percent)

Mean ത𝑋 is used when you want to show the average response

Median ෨𝑋 is used when you want to show middle data or response

Mode 𝑋is used when you want to show the most frequently occurring

response

Standard Deviation SD is used when you want to show how "spread out" the data are

▪ Sample Research Questions for Frequencies:

Statistical Tests

✓How many respondents like the given various brands of mobile phone?

✓What is the demographic profile of the respondents in terms of gender and grade level?

▪ Sample Research Questions for Mean (with standard deviation):

✓What is the level of anxiety of the senior high school students?

✓What is the level of political awareness of the college students?

✓What is the average grade of the students in Math?

▪ Sample Research Questions for Median:

Statistical Tests

✓What is the middle age of the participants of the study?

▪ Sample Research Questions for Mode:

✓What flavor of ice cream that most elementary students like?

✓What is the popular mobile phone brand among senior high school students?

Statistical Tests

Statistics That Look at Differences

Parametric Test

(Interval/ Ratio)

Non-Parametric Test

(Nominal/ Ordinal)

Test

StatisticPurpose

Number of

Groups

Independent samples

t-testMann-Whitney U Test t

to test the difference between the means

of two independent groups2

Paired samples t-test

(dependent t-test)

Wilcoxon Signed Rank

Testt

to test the difference between the means

from two paired groups (such as before-

and-after observations on the same

subject)

2

Chi-Square Test Fisher’s Exact Test 𝑋2 to analyze nominal and ordinal data to

find differences between groups2 or more

Statistical Tests

Statistics That Look at Differences

Parametric Test

(Interval/ Ratio)

Non-Parametric Test

(Nominal/ Ordinal)

Test

StatisticPurpose

Number of

Groups

One-way Analysis of

Variance (ANOVA)Kruskal-Wallis Test F

to test the difference among means of

more than two independent groups for

one independent variable

3 or more

Two-way Analysis of

Variance (ANOVA)Kruskal-Wallis Test F

to test the difference among means for

two independent variables, of which each

can have multiple levels

3 or more

Repeated Measures

ANOVAFriedman Test F

To test the difference among means in the

same group over time (extended paired t-

test)

1

▪ Sample Research Questions for Independent samples t-test/ Mann-Whitney U test:

Statistical Tests

✓ Is there a significant difference in the level of emotional intelligence by gender among high school students?

✓ Is there a significant difference in the academic performance by grade level among senior high school students?

✓ Is there a significant difference between the Mathematics test score of pupils who have had early Mathematicsexposure and those pupils without?

▪ Sample Research Questions for Paired samples t-test/ Wilcoxon Signed rank test:

✓Is there a significant difference in the Science scores of the students before and after ateaching intervention?

✓Is there a significant difference in the plant growth after a synthetic fertilizer has beenintroduced?

▪ Sample Research Questions for Chi Square test/ Fisher’s Exact test:

Statistical Tests

✓Is there a significant difference in the religious affiliation and educational background amongsenior high school students?

✓Is there a significant difference in mobile phone brand preference by gender among highschool students?

▪ Sample Research Questions for One-way ANOVA/ Kruskal-Wallis test:

✓Is there a significant difference in the social skills of the senior high school students by theirstrand?

✓Is there a significant difference in the political participation among respondents in terms oftheir age group?

▪ Sample Research Questions for Two-way ANOVA:

Statistical Tests

✓Is there a significant difference between the income and gender for anxiety level at jobinterviews?

✓Is there a significant difference between the grade level and strand for study skills levelamong high school students?

▪ Sample Research Questions for Repeated measures ANOVA/ Friedman test:

✓Is there a significant difference in the blood pressure at a training program at three timepoints (pre-, midway, post exercise intervention)?

▪Post Hoc Tests

Statistical Tests

✓A post hoc test is used only after we find a statistically significant result and need todetermine where our differences truly came from. The term “post hoc” comes from the Latinfor “after the event”.

▪Bonferroni Test – is perhaps the simplest post hoc analysis. A Bonferroni test isa series of t -tests performed on each pair of groups.

▪ Tukey’s Honest Significant Difference (HSD) Test – is a very popular post hocanalysis. This analysis, like Bonferroni’s, makes adjustments based on the number ofcomparisons, and these comparisons give us an estimate of the difference betweenthe groups and a confidence interval for the estimate.

Statistical Tests

Statistics That Look at Associations

Parametric Test

(Interval/ Ratio)

Non-Parametric Test

(Nominal/ Ordinal)Purpose

Pearson-Product Moment

Correlation (r-value)

Spearman Rank-Order

Correlation (𝜌-value)

to measure the strength and direction of the

relationship between two variables

-Chi Square Test for

Independence (Nominal data)to measure the relationship of two nominal data

Linear Regression -

to predict the value of a dependent variable and

measure the size of the effect of the independent

variable on a dependent variable while controlling

for covariates

▪ Sample Research Questions for Pearson-r Correlation:

Statistical Tests

✓Is there a significant relationship between the emotional intelligence and problem-solvingskills of the high school students?

✓Is there a significant relationship between the financial literacy and financial participation ofemployees?

▪ Sample Research Questions for Spearman Signed Rank test:

✓Is there a significant relationship between financial literacy and educational attainment amongresidents of Davao City?

✓Is there a significant relationship between the level of anxiety and grade level senior highschool students?

▪ Sample Research Questions for Chi Square Test for Independence:

Statistical Tests

✓Is there a significant relationship between gender and drunk driving (drunk or not drunk)?

✓Is there a significant relationship between voter intent and political party membership?

▪ Sample Research Questions for Linear Regression:

✓Which of the emotional intelligence dimensions has an influence on the analytical problem-solving skills of students in General Mathematics?

✓Does customer satisfaction influence loyalty?

Correlation

➢It is a statistical tool used to measure the association

of two quantitative variables.

➢It is concerned with the relationship in the change

and movements of two variables.

➢It measures the extent to which the points cluster

about a straight line.

Correlation

➢Correlation coefficients vary from -1 to +1.

➢The positive values indicate an increasing

relationship.

➢The negative values indicate a decreasing

relationship.

Correlation

➢Positive Correlation is said to occur when:

➢ there is an increase in the values of the first variable

as the values of the second variable increase.

➢there is a decrease in the values of the first variable as

the values of the second variable decrease.

Correlation

➢Negative Correlation is said to occur when:

➢ there is an increase in the values of the first variable

as the values of the second variable decrease(or vice

versa).

Correlation

Correlation

Range Interpretation

±1.00 Perfect Correlation

±0.91 to ±0.99 Very high positive/ negative correlation

±0.71 to ±0.90 High positive/ negative correlation

±0.51 to ±0.70 Moderately positive/ negative correlation

±0.31 to ±0.50 Low positive/ negative correlation

±0.01 to ±0.30 Slight correlation, negligible positive/ negative correlation

0 No correlation

Statistical Tests