SAMRA A. AKMAD INSTRUCTOR

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 scaleExample : 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 CALCULATORUse the formula:

t= X1 – X2

SS1 + SS2 1 + 1 n1 + n2 -2 n1 + n2

Where :t=testX1 = 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 EXCELSTEP 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

between the performance of the male and the female AB students in spelling.

H1 : There is a significant difference between the performance of the male and the female AB students in spelling.

III. LEVEL OF SIGNIFICANCE:a = 0.05df = n1 + n2 - 2

= 10 + 10 – 2 = 18t-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