Advanced statistics Lesson 1

A Mathematical science concerned with
data collection, presentation, analysis
and interpretation. It is the only
mathematical field required for many
social sciences.
A system collection of data on
measurements or observations often
related to demographic information
such as population counts, incomes,
population counts at different ages,
and etc.

DESCRIPTIVE STATISTICS- deals with the
presentation and collection of the data. This is
usually the first part of a statistical analysis.
 While drawing a conclusions, one needs to be
very careful so as not to draw the wrong or
biased conclusion
INFERENTIAL STATISTICS- as the name suggests,
involves drawing the right conclusions from
the statistical analysis that has been
performed using descriptive statistics . In the
end, it is the inference that makes the studies
important.

 Can be solved using parametric tests and
non-parametric tests.

Tests applied to data that are
normally distributed, the levels
of measurement of which are
expressed in interval and ratio

 As the name implies, non- parametric tests
do not require do not require parametric
assumptions because interval data are
converted to rank-ordered data
NON-PARAMETRIC TESTS ARE:
 Wilcoxon signed rank test
 Whitney-Mann- Wilcoxon test
 Kruskal-Wallis test
 Friedman’s test

 t-test for Independent Samples
 t-test for Correlated Sample
 z-test for Two Sample Means
 z-tests for One Sample Group
 F-test (ANOVA)
 Pearson Product Moment Coefficient of
Correlation
 Simple Linear Regression Analysis
 Multiple Regression Analysis

We use parametric tests when
 the distribution is normal, that is when
skewness is equal to zero and kurtosis
equals .265
SK= 3 ( X-Md )
SD
Ku= ___Q___
P90- P10
where : Q= Q3 – Q1
2

 the level of measurement to be analyzed are
expressed in interval and ratio data.
INTERVAL DATA – Provide numbers that reflect
differences among items .
Example: Intelligence tests
RATIO DATA - Highest type of scale
Example : Measures of weight

 USING A SCIENTIFIC
CALCULATOR
 USING A MICROSOFT OFFICE
EXCEL

A Test of difference between
two independent groups. The
means are compared X1 against
the X2.

 When we compare the means of
two independent samples
When the data are normally
distributed, Sk=0 and Ku=.265
When data are expressed in
interval and ratio data
When the sample is less than 30

o BY USING SCIENTIFIC CALCULATOR
Use the formula:
t= X1 – X2
SS1 + SS2 1 + 1
n1 + n2 -2 n1 + n2
Where :
t=test
X1 = mean of group 1
X2 = mean of group 2
SS1 = sum of squares of group 1
SS2 = sum of squares of group 2
n1 = no. of observations of group 1
n2 = no. of observations of group 2

o BY USING MICROSOFT EXCEL
STEP 1-Enter the data in the excel
STEP 2- Click Tools on the Menu Bar and select Data Analysis
STEP 3- The Data Analysis dialogue will appear.
Then, select t-test: two-sample assuming equal variances(
if the no. of observations of two groups are equal) or t-
test: two-sample assuming unequal variances( if the no. of
observations of two groups are not equal)
STEP 4- Enter the values of the Variable Range 1 and Variable
Range 2 .Then enter the level of significance of 0.05 in the
Alpha
STEP 5 – On the output option select output range. Then,
click anywhere in the blank worksheet and click OK.

The following are the scores in spelling of 10
male and 10 female AB students. Test the
null hypothesis that there is no significant
difference between the performance of male
and female AB students in spelling. Use the
t-test at 0.05 level of significance.
MALE ( X1 ) : 14, 18, 17, 16, 4, 14, 12, 10, 9, 17
FEMALE ( X2 ) : 12, 9, 11, 5, 10, 3, 7, 2, 6, 13

I. PROBLEM: Is there a significant difference
between the performance of the male and
the female AB students in spelling?
II. HYPOTHESES:
H0 : There is no significant difference
the female AB students in spelling.
H1 : There is a significant difference
the female AB students in spelling.

III. LEVEL OF SIGNIFICANCE:
a = 0.05
df = n1 + n2 - 2
= 10 + 10 – 2
= 18
t-tabular value 0.05 = 2.101
IV. STATISTICS : t-test for two independent
samples
V. DECISION RULE: If the t-computed value is
greater than or beyond the t-tabular /
critical value , disconfirm/reject the null
hypothesis

VI. CONCLUSIONS :
Since the t-computed value of 2.88 is greater
than the t-tabular value of 2.101 at 0.05
level of significance with 18 degrees of
freedom, the null hypothesis is disconfirmed
or rejected in favor of the research
hypothesis . This means that there is a
significant difference between the
performance of the male and the female AB
students in spelling implying that the male
students performed better than the female
students considering that the mean/average
score of the male students of 13.1 is greater
compared to the average score of female
students of only 7.8

Two groups of experimental rats were
injected with a tranquilizer at 1.0 mg and
1.5 mg. dose respectively. The time given in
seconds that took them to fall asleep is
herby given. Use the t-test for independent
samples at 0.01 to test the null hypothesis
that there is no significant difference
brought about by the dosages on the length
of time it took for the rats to fall asleep.
1.0 mg dose( X1 ) : 9.8, 13.2, 11.2, 9.5,13.0,
12.1, 9.8, 12.3, 7.9, 10.2, 9.7
1.5 mg dose ( X2: ) : 12.0, 7.4, 9.8, 11.5, 13.0,
12.5, 9.8, 10.5, 13.5

To find out whether a new serum would
arrest leukemia, 16 patients on the advanced
stage of the disease were selected. Eight
patients received treatment and eight did
not. The survival was taken from the time
the experiment was conducted.
No treatment ( X1 ): 2.1, 3.2, 3.0, 2.8, 2.1,
1.2,1.8, 1.9
With treatment ( X2 ) : 4.2, 5.1, 5.0, 4.6, 3.9,
4.3, 5.2, 3.9

Advanced statistics Lesson 1

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Advanced statistics Lesson 1