BASIC STATISTICS

By: Aledel Christian Alejandro

STATISTICS – is a branch of mathematics that deals with the

collection, organization, presentation, analyzation and

interpretation of numerical data.

Kind of Statistics

1. Descriptive Statistics - used to describe the basic features of data in a study.

A. Measure of Central TendencyB. Measure of Dispersion

2. Inferential Statistics – used to make judgment, observe difference between groups , draw inferences, reach conclusion beyond the immediate data.

a. Hypothesis Testingb. Correlation

COLLECTING DATA

Sample Versus Population

Calculating Sample Size

Slovin’s Formula

sample N size 1 + Ne2

N = populatione = margin of error

Levels of Data

1. Nominal – qualitative data expressed in categories, labels, names, etc. (gender,

nationality)

2. Ordinal – quantitative or qualitative data whose order is specified however,

differences between values are meaningless. (educational attainment, ID number)

1. Interval – quantitative data arranged in a specific order whose differences between values are meaningful but the presence of

“zero” does not necessarily mean “nothing”. (grades, IQ)

2. Ratio – quantitative data arranged in a specific order whose differences between values are meaningful and the presence of

“zero” means “nothing”. (physical quantities)

ANALYZING and INTERPRETING DATA

NORMAL DISTRIBUTION

Test of Normality1. Skewness and Kurtosis are equal or approximate to zero.

2. P-value > 0.05 in the Shapiro-Wik test for normality

One-Tailed or Two-Tailed Test?

One-Tailed Test – testing for the possibility of the relationship in one direction and

completely disregarding the possibility of the relationship on the other direction.

Two-Tailed Test – testing for the possibility of the relationship in both direction.

DESCRIPTIVE STATISTICS

Central Tendency

- relates to the way in which quantitative data tend to cluster around some value.

1. Mean 2. Median3. Mode

Mean – common “average” and always assumes that the distribution is normal.

Note:- do not use mean if there are presence of

extreme scores- can only be used under interval or ratio level

data

Median – middlemost score and is not affected by extreme scores.

Note:- use median if there are presence of extreme

scores or the distribution is skew.- can be used under interval or ratio level data

Mode – frequently occurring data.

Note:- best use for nominal data and

ordinal data.

Dispersion

1. Range – highest value minus lowest value.

2. Standard Deviation - shows the relation that set of scores has to the mean

of the sample. Tells about the homogeneity or heterogeneity of the

data.

Inferential Statistics

Hypothesis Testing

Two Kinds of Hypotheses

1. Null Hypothesis (H0)*There is no significant difference

_______________

2. Alternative (Ha)*There is a significant difference

_______________

Test of Significance

Alpha Level - specifies the probability level for our evidence to be an unreasonable estimate.

Probability Value (P-value) – is a measure of how much evidence

we have against the null hypothesis.

If the probability value (P-value) is greater than 0.05, there is no significant difference.

We fail to reject the H0.

P > 0.05

If the probability value (P-value) is less than 0.05, there is a significant difference. We reject

the H0.

P < 0.05

T

TEST

One Sample t-test

- compares the mean score of a sample to a known value. Usually, the known value is a population

mean.

t-test for Independent Samples

- compares the mean scores of two groups on a given variable. Used for two groups

that are unrelated.

Note: Independent variable in this test must be dichotomous.

t-test for Dependent Samples (Paired Sample)

- compares the means of two variables. It computes the difference between the two

variables for each case, and tests to see if the average difference is significantly different from

zero.

CORRELATION- is a statistical technique that can show whether and

how strongly pairs of variables are related.

1. Pearson R - tells you the magnitude and direction of the association between two variables that are on an interval or ratio

scale. Both variables are normally distributed.

2. Spearman Rho- tells you the magnitude and direction of the association between two variables that are on an interval or

ratio scale. Both variables are NOT normally distributed.

Correlation Coefficient ranges from -1 to +1.

1. Positive correlation means that the two variables are directly related to

each other.

2. Negative correlation means that the two variables are inversely related to

each other.