data analyzing

1. Introduction: Inferential statistics

2. Definitions
• Inferential statistics permits generalization from samples to
populations.
• Sampling error is main problems that faces the challenge of
generalizing from samples to populations. Sampling error involves
the role of chance in deciding on the findings or results.
• Inferential statistics deals with the sampling error. They are used to
estimate the role of chance in the findings, such as differences
between groups, relation between two groups and deciding
whether the difference or the relationship is a significant finding or
a result of chance only.
• The other way to check that chance had nothing to do with the
findings is to repeat the study several times, which can become
awkward, time-consuming and impractical.

3. Definition
• Population or universe : the entire group of items under examination (everyone in your
statistics class, all students at JU, all teachers in Jiren High School ( JHS) etc.).
• Sample : a group taken from the population (a sample of 10 students in your statistics
class, 1000 randomly selected students at JU, 5 female teachers selected by purposive
sampling at JHS).
• Parameter: an objective measure that describes some characteristic of the population
(average score on the attitude of students towards PE in JU , average age of students at
JU, average endurance score of of female students at JU)
• Statistic : an objective measure that describes some characteristic of the sample
(average PE attitude score of 350 randomly selected students, average age of 1000
randomly selected students from JU, average income of 5 female teachers selected by
purposive sampling at JHS).
• Statistical inference : the process of using data obtained from a sample to make
estimate and test hypotheses about the characteristics of a population

4. Purpose of Inferential statistics
• Although there are various uses of statistical
techniques, some very common situations
psychological research are:
1. Infer (or estimate) parameters, such as the
mean and the variance, of the populations
based on their samples.
2. Compare the inferred parameters of the
populations: are they significantly different

5. The concept and procedures of hypothesis
testing
•Hypothesis testing involves making inferences
about the nature of a population on the basis of
observations of a sample drawn from a
population
• The logic of hypothesis testing follows the chain
of reasoning in inferential statics as shown below
.

6. Cont’d
• Chain of reasoning in HT

7. Cont’d
• The process of HT involves determining the difference
between the hypothesized value of the population
(parameter) and the value of the sample selected from
the population (statistic ) .
• If the difference b/n the parameter and the statistic is
very large we reject the hypothesis or we retain the
hypothesis if the difference b/n the parameter and the
statistic very small.
• In other words HT involves determining the magnitude
of the difference b/n the observed value of the
statistic ( for example mean) and the hypothesized
value of the parameter ( for example µ ) .

8. • Cont’d
Population value
( parameter )
Magnitude of
the difference
b/n
the observed
statistic and
the
hypothesized
parameter?
Small
difference
Large
difference
Don’t
Reject
p >.05
Reject
p<.05

9. TYPE OF TEST
• One sample t test
• Independent sample t or z test
• ANOVA
• Linear and Multiple Regression analysis
• Non parametric statistics

10. One sample t or z test
• One sample t test helps us to conduct
hypothesis test whether a sample mean is
significantly differ from a known population
mean.
• T test : is used to test hypothesis about known
population mean (µ) when the value of σ is
unknown.
Z = (Mean-µ)/σmean , where σmean = S2/√n

11. Example
• The endurance score of a general population (µ) of football players
as measured by a Coopper test is normally distributed with a mean
3000 meter. The researcher suspects that the endurance level of
football players in country x is less than the general population. The
researcher administered a Coopper test for 45 participants. The
data are indicated as follows.
• 3000,2000,2500,3000,3500,2000,1500,4000,3000,3500,
3000,2000,3000,4500,2000,1000,2500,2800,2000,3000,
3200,3000,2800,4000,3000,1500,2000,2400,2000,3000,
4000,2000,2500,3000,3000,3100,3200,3000,3200,2500,
4000,3200,1500,2000,3200

12. Question
• Test the hypothesis that the observed mean is
significantly less than from the hypothesized
value.
• Ho: µ= 3000
• H1: µ < 3000

13. Cont’d
One-Sample Statistics
N Mean
Std.
Deviation
Std. Error
Mean
copte
45 2757.78 761.425 113.507

14. Cont’d
One-Sample Test
Test Value = 3000
t df
Sig. (2-
tailed)
Mean
Difference
95% Confidence
Interval of the
Difference
Lower Upper
copte -2.134 44 .038 -242.222 -470.98 -13.46

15. Conclusion
• Reject Ho as p<.05

16. Reporting the results
• The mean score the endurance level of
football players in country x was found to be
2757.78 with a standard deviation of 761.425
as indicated in table ….below. The one sample
t test indicates that the the endurance level of
football players in country x was significantly
less than the endurance score of a general
population of football players as measured by
a Copper test , t(44)= -2.134, p<.05.

17. Cont’d
One-Sample Statistics
N Mean
Std.
Deviation
Std. Error
Mean
copte
45 2757.78 761.425 113.507

18. SPSS
• Data entry
1. Enter all the scores from the sample in one column of the
data editor, var0001
Data analysis
1. Click analyse, select compare means, and click on one
sample t test
2. Highlight the column label for the set of scores (var0001) in
the left box and click the arrow to move it into the test
variable box
3. In the Test value at the bottom of one sample t Test
window , enter the hypothesized value for the population
mean from the null hypothesis.
4. Click OK

19. SPSS output
• The program will produce a table of one sample
statistics showing the number of scores , the
sample mean and the standard deviation , the
estimated standard error and the mean.
• A second table produce the results of One
Sample Test, including the value of t, the degree
of freedom , the level of significance (the p-value
or alpha level for the test ) and the size of the
mean difference b/n the sample mean , the
hypothesized population mean and the
confidence interval.

20. Activity
• The mean attitude score towards PE for the
general population of students in JHS is normally
distributed with a mean of 3.5. The researcher
believes that the mean attitude score towards PE
for students who actively participate in PE class
is grater than the mean attitude score of the
general population of students. The researcher
selects 30 students and administered an attitude
scale. The data are indicated as follow. Note: the
higher the score the higher the attitude

21. Cont’d
• 3,3,4,2,3,4,5,2,4,4,4,2,1,3,4,5,5,2,4,2,5,4,4,5,4,
2,1,1,2,3,4,5,4,3,4
Question
• Test the hypothesis that the observed mean is
significantly different from the hypothesized
value.

22. Independent sample t test
• The independent sample t test helps us to
check whether two groups of means differ
significantly.
• t= (Mean1-Mean2 )/ Smean1-Smean2 ,
• where Smean1 and Smean2 is the estimated standard error for
the two means.

23. Activity
1. A researcher wants to determine whether players perform better a football skill
with lecture methods or with both lecture and demonstration. Ten players are
randomly assigned to two experimental condition; their scores on skill
performance are given below.
____________________________________________________________________
Lecture Lecture +Demonstration Lecture Lecture + Demonestration
(Group 1) (Group 2) (Group 1) (Group 2)
___________________________________________________________________
8 4 9 6
10 8 10 15
7 7 11 11
12 10 6 9
6 12 13 8
____________________________________________________________________

24. Question
• Test whether the two means are statistically
significantly different
• Ho: µlecture =: µlecture+ demon
• H1: µlecture ≠ : µlecture+ demon

25. Cont’d
Group Statistics
VAR0
0002 N Mean
Std.
Deviatio
n
Std.
Error
Mean
skillper 1 10 9.2000 2.44040 .77172
2 10 9.0000 3.16228 1.00000

26. Cont’d
Independent Samples Test
Levene's Test
for Equality of
Variances t-test for Equality of Means
F Sig. t df
Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
skillper Equal
variances
assumed
.313 .583 .158 18 .876 .20000 1.26315 -2.45379 2.85379
Equal
variances not
assumed
.158 16.913 .876 .20000 1.26315 -2.46606 2.86606

27. Conclusion
• Fail to reject Ho as p>.05

28. Reporting the result
• As indicated in the table ……., the groups that
has been taught with lecture methods
perform better (M=9.2 , S=2.44) than the
group that has been taught with lecture and
demonstration (M= 9.0, S=3.16). This
differences was not statistically significant,
t(18)=.158, P>.05.

29. SPSS
• Data entry
1. The scores are entered in what is called stacked format ,
which means that all the scores from both
samples/groups are entered in one column of the data
editor (var00001). Enter the scores for the sample/group 2
directly beneath the scores from sample/group 1 with no
gaps.
2. Values are then entered into a second column (var00002)
to identify the sample or treatment condition
corresponding to each of the scores. For example enter a
1 beside each score from sample/group 1 and enter a 2
besides each score from sample/group 2.

30. Data Analysis
1. Click analyze, select compare means, and click in independent sample t
test.
2. Highlight the column label for the set of scores (var00001) in the left
box and click the arrow to move it into the test variables box
3. Highlight the column label for the set of scores (var00002) in the left
box and click the arrow to move it into the group variable box
4. Click on define groups
5. Assuming that you used the numbers 1 and 2 to identify the two set
of scores , enter the values 1 and 2 into appropriate group box.
6. Click continue
7. Click OK

31. SPSS output
• SPSS produce summery table showing the
number of scores , the mean , the standard
deviation , and the standard error of the two
samples.
• T values , degrees of freedom , p, size of the
mean difference and CI are displayed on the
second table

32. Activity
• A researcher wants to conduct study entitled “Sex difference as a function
of Anxiety before a major competition”
• Anxiety scores (Y) Sex (X ; Male coded 1, Femle code 0)
• 15.00 male
• 25.00 male
• 12.00 male
• 20.00 male
• 20.00 female
• 16.00 female
• 18.00 female
• 22.00 female
• 20.00 female
• 12.00 female

33. Question
• Test whether the two means are statistically
significantly different