Basic statistics presentation
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BASIC STATISTICS
By: Aledel Christian Alejandro
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STATISTICS – is a branch of mathematics that deals with the
collection, organization, presentation, analyzation and
interpretation of numerical data.
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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
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2. Inferential Statistics – used to make judgment, observe difference between groups , draw inferences, reach conclusion beyond the immediate data.
a. Hypothesis Testingb. Correlation
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COLLECTING DATA
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Sample Versus Population
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Calculating Sample Size
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Slovin’s Formula
sample N size 1 + Ne2
N = populatione = margin of error
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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)
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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)
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ANALYZING and INTERPRETING DATA
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NORMAL DISTRIBUTION
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Test of Normality1. Skewness and Kurtosis are equal or approximate to zero.
2. P-value > 0.05 in the Shapiro-Wik test for normality
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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.
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DESCRIPTIVE STATISTICS
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Central Tendency
- relates to the way in which quantitative data tend to cluster around some value.
1. Mean 2. Median3. Mode
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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
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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
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Mode – frequently occurring data.
Note:- best use for nominal data and
ordinal data.
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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.
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Inferential Statistics
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Hypothesis Testing
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Two Kinds of Hypotheses
1. Null Hypothesis (H0)*There is no significant difference
_______________
2. Alternative (Ha)*There is a significant difference
_______________
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Test of Significance
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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.
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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
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T
TEST
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One Sample t-test
- compares the mean score of a sample to a known value. Usually, the known value is a population
mean.
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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.
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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.
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CORRELATION- is a statistical technique that can show whether and
how strongly pairs of variables are related.
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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.
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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.