Study on Self-Esteem and Statistical Analyses

Answered

Answer all questions.

A researcher conducted a study to measure Self-Esteem among of a group of 16 year old students. The sample consisted of 120 subjects; 60 males and 60 female subjects. In her study, the researcher defined Self-Esteem as consisting of three factors or constructs; namely, Physical Self-Esteem, Academic Self-Esteem and Social Self-Esteem.

State three hypotheses using Emotional Intelligence as the dependent variable for the following:

i) Comparison according to Gender (Male & Female)
ii) Comparison according to Socioeconomic Status (High, Middle & Low)
iii) Comparison according to Types of school (Rural & Urban)

State the appropriate statistical tests to test the three hypotheses listed in Question 2. Give reasons.

State the assumptions required for the statistical test(s) used in Question 3.

Explain what is meant by the ‘normality assumption’?

A physical education teacher collected data on students’ height and the span of jump (see Table 1 below):

Student	Height (m)	Span of jump (m)
1	1.63	2.34
2	1.80	2.48
3	1.75	2.29
4	1.86	2.62
5	1.83	2.64
6	1.71	2.30
7	1.75	2.44
8	1.96	2.67
9	1.60	2.39
10	1.68	2.47
11	1.80	2.60
12	1.87	2.75
13	1.74	2.40
14	1.67	2.46
15	1.64	2.33

What statistical procedure would you use to predict length of jump using height? Give reasons.
Explain clearly two assumptions that must be met in conducting the test that you have identified in Q5 (a). Why it is important these assumptions are met?

A researcher was interested in finding out whether attitude towards English would be enhanced when students were taught using the iPad.

Table 1 : Mean Attitude Score before and after the intervention
	N	Mean	Std. Deviation	Std. Error Mean
Pretest	30	18.50	5.33	0.97
Posttest	30	23.86	4.75	0.87

Table 2 : Paired t Test
	Mean	Std. Deviation	Std. Error Mean	Lower	Upper	t	df	Sig. (2 tailed)
Pretest	-5.36	2.90	0.62	-6.65	-4.08	-8.66	29	.000
Posttest

Referring to Table 1 and Table 2, answer the following questions:

Why was the t-test used to analyse the data?
State the assumptions that should be met to use the t-test.
State ONE null hypothesis.
State the alternative hypothesis.
What can you conclude from the two tables?

A study was conducted to assess the logical reasoning ability of male and female undergraduates. The results of the study is shown in Table 1 and 2.

Table 1

Gender	N	Mean Score on the Logical Reasoning Test	Standard deviation	p-value
Male	35	72	7.2	0.0005
Female	40	82	7.4	0.0005

See Table 1 and answer the following questions:

What is the statistical test used?
Suggest one null hypothesis.
What can you conclude?

Table 1:
	Gender	Kolmogorov-Smirnov^a			Shapiro-Wilk
	Gender	Statistic	df	Sig.	Statistic	df	Sig.
Spatial Test Scores	Male	0.879	34	0.012	0.971	78	0.016
Spatial Test Scores	Female	0.185	39	0.001	0.079	96	0.008
a. Lilliefors Significance Correction

See Table 1 above and answer the following:

What is the purpose of the statistical test used?
Explain the difference between ‘Kolmogorov-Smirnov’ and ‘Shapiro-Wilk’.
What can you conclude?

	Spatial Reasoning	Memory	Metacogniton	Mathematical ability	Verbal reasoning
Spatial reasoning
Memory	0.56
Metacognition	0,65	0.67
Mathematical ability	0.43	0.60	0.59		.
Verbal reasoning	0.34	0.41	0.49	0.70

A study was conducted to determine the relationships between spatial reasoning, memory, metacognition, mathematical ability and verbal reasoning. The sample consisted of 80 males and 80 female 16 year old students. The Table above shows a correlation matrix between the five variable. Based on the table answer the following questions: