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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.