Figure 5.5: Tests of Within-Subjects Effect Measure: MEASURE 1 Tests of Within-Subjects Effects Type III Sum Source of Squares df Mean Square F Sig Partial Eta Squared Time Sphericity Assumed 282.013 3 141.007 58.228 .000 543 Greenhouse-Geisser 282.013 1.782 158.227 58.228 .000 543 Huynh-Feldt 282.013 1.845 152.852 58.228 .000 543 Lower-bound 282.013 1.000 282.013 58.228 .000 go 543 Error Sphericity Assumed 237.320 597 2.422 (Time) Greenhouse-Geisser 237.320 87.335 2.717 Huynh-Feldt 237.320 90.405 2.625 Lower-bound 237.320 199.000 4.843 Table 5.1: Excerpt of scores obtained by study participants in each of the tests Participant # Pre-training score Post-training 1 Post-training 2 score score Post-training 3 score 1 5 7 .8 2 4 6 7 9 3 6 7 8 9 4 4 7 7 5 5 8 8 B B 5 B 6 7 7 6 5 8 6 7 7 7 9 6 6 8 8 200 7 8 8 The study data was analysed using IBM SPSS Statistics version 26 and the output showed in Figure 5.1 to Figure 5.5 was produced Figure 5.1: Test of Normality of Employees Competence Scores measured on & occasions Tests of Normality Kolmogorov Smimov Shapiro-Wilk Statistic d Sig. Statistic df Sig Pre Training Score 090 200 084 985 200 323 Post Training1 Score 136 200 079 987 200 469 Post Training2 Score Post Training Score 072 200 .200° 992 200 855 082 200 097 964 200 407 "This is a lower bound of the true significance a Lillefors Significance Correction Figure 5.2: Dependent Variable measured on 4 occasions Measure: MEASURE_1 Within-Subjects Factors Time Dependent Variable 1 Pre Training Score 2 Post Training1 Score 3 Post Training2 Score 4 Post Training3 Score Figure 5.3: Descriptive Statistics of the Dependent Variable measured on 4 occasions Descriptive Statistics Pre Training Score Post Training Score Post Training2 Score Post Training Score Figure 5.4: Test of Sphericity Mauchly's Test of Sphericity" Measure: MEASURE 1 Mean Std. Deviation N 5.010 81438 200 6755 95894 200 7.240 86959 200 7.930 79893 200 Epsilon Within Subjects Effect Mauchly's W Approx. Chi- Square df Sig Greenhouse Geisser Huynh-Feld Lower bound Time 878 6.252 5 104 .891 923 500 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. a. Design: Intercept Within Subjects Design: Time b. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within Subjects Effects table.

Figure 5.5: Tests of Within-Subjects Effect Measure: MEASURE 1 Tests of Within-Subjects Effects Type III Sum Source of Squares df Mean Square F Sig Partial Eta Squared Time Sphericity Assumed 282.013 3 141.007 58.228 .000 543 Greenhouse-Geisser 282.013 1.782 158.227 58.228 .000 543 Huynh-Feldt 282.013 1.845 152.852 58.228 .000 543 Lower-bound 282.013 1.000 282.013 58.228 .000 go 543 Error Sphericity Assumed 237.320 597 2.422 (Time) Greenhouse-Geisser 237.320 87.335 2.717 Huynh-Feldt 237.320 90.405 2.625 Lower-bound 237.320 199.000 4.843 Table 5.1: Excerpt of scores obtained by study participants in each of the tests Participant # Pre-training score Post-training 1 Post-training 2 score score Post-training 3 score 1 5 7 .8 2 4 6 7 9 3 6 7 8 9 4 4 7 7 5 5 8 8 B B 5 B 6 7 7 6 5 8 6 7 7 7 9 6 6 8 8 200 7 8 8 The study data was analysed using IBM SPSS Statistics version 26 and the output showed in Figure 5.1 to Figure 5.5 was produced Figure 5.1: Test of Normality of Employees Competence Scores measured on & occasions Tests of Normality Kolmogorov Smimov Shapiro-Wilk Statistic d Sig. Statistic df Sig Pre Training Score 090 200 084 985 200 323 Post Training1 Score 136 200 079 987 200 469 Post Training2 Score Post Training Score 072 200 .200° 992 200 855 082 200 097 964 200 407 "This is a lower bound of the true significance a Lillefors Significance Correction Figure 5.2: Dependent Variable measured on 4 occasions Measure: MEASURE_1 Within-Subjects Factors Time Dependent Variable 1 Pre Training Score 2 Post Training1 Score 3 Post Training2 Score 4 Post Training3 Score Figure 5.3: Descriptive Statistics of the Dependent Variable measured on 4 occasions Descriptive Statistics Pre Training Score Post Training Score Post Training2 Score Post Training Score Figure 5.4: Test of Sphericity Mauchly's Test of Sphericity" Measure: MEASURE 1 Mean Std. Deviation N 5.010 81438 200 6755 95894 200 7.240 86959 200 7.930 79893 200 Epsilon Within Subjects Effect Mauchly's W Approx. Chi- Square df Sig Greenhouse Geisser Huynh-Feld Lower bound Time 878 6.252 5 104 .891 923 500 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. a. Design: Intercept Within Subjects Design: Time b. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within Subjects Effects table.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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Related questions

Question

Study the information provided below and answer the questions below.
ABC Limited (a pseudonym for confidentiality purposes), an information technology company based in a Southern African country, initiated a continuous improvement process last year to sharpen its competitive edge. As part of this effort, the company which employs 500 employees conducted three comprehensive training sessions for a randomly selected sample of employees during the financial year ended 31 December 2023. The effectiveness of this training programme was assessed at the end of the financial year. At the outset of the programme, 200 employees were randomly selected from a pool of 410 employees who volunteered to participate in a study. These 200 participants were assessed for their baseline competence using a standardized measurement
instrument, with scores ranging from 1 (lowest) to 10 (highest). Subsequently, the same instrument was used to test the participants after each of the three training sessions. The results of these tests are detailed in Table 5.1.
Notably, there was no attrition among participants throughout the continuous improvement programme.

5.1 Identify the independent variable (IV) and dependent variable (DV) for the evaluation, then state the underlying
research question and formulate both the null and alternative hypotheses.
5.2 Critically discuss three parametric assumptions that guided the selection of a statistical analysis to evaluate the
effectiveness of ABC’s training programme. Using the output provided in Figures 5.1 to 5.5, determine whether a
parametric or non-parametric test was employed for the impact evaluation and substantiate your conclusion.
5.3 Using the standard reporting format, provide a detailed interpretation of the output of the inferential statistical tests conducted in the evaluation and state whether the intervention led to a significant improvement in employee scores.

Figure 5.5: Tests of Within-Subjects Effect
Measure: MEASURE 1
Tests of Within-Subjects Effects
Type III Sum
Source
of Squares
df
Mean Square
F
Sig
Partial Eta
Squared
Time
Sphericity Assumed
282.013
3
141.007
58.228
.000
543
Greenhouse-Geisser
282.013
1.782
158.227
58.228
.000
543
Huynh-Feldt
282.013
1.845
152.852
58.228
.000
543
Lower-bound
282.013
1.000
282.013
58.228
.000
go
543
Error
Sphericity Assumed
237.320
597
2.422
(Time)
Greenhouse-Geisser
237.320
87.335
2.717
Huynh-Feldt
237.320
90.405
2.625
Lower-bound
237.320
199.000
4.843

Table 5.1: Excerpt of scores obtained by study participants in each of the tests
Participant #
Pre-training score Post-training 1 Post-training 2 score
score
Post-training 3 score
1
5
7
.8
2
4
6
7
9
3
6
7
8
9
4
4
7
7
5
5
8
8
B
B
5
B
6
7
7
6
5
8
6
7
7
7
9
6
6
8
8
200
7
8
8
The study data was analysed using IBM SPSS Statistics version 26 and the output showed in Figure 5.1 to Figure 5.5 was
produced
Figure 5.1: Test of Normality of Employees Competence Scores measured on & occasions
Tests of Normality
Kolmogorov Smimov
Shapiro-Wilk
Statistic
d
Sig.
Statistic
df
Sig
Pre Training Score
090
200
084
985
200
323
Post Training1 Score
136
200
079
987
200
469
Post Training2 Score
Post Training Score
072
200
.200°
992
200
855
082
200
097
964
200
407
"This is a lower bound of the true significance
a Lillefors Significance Correction
Figure 5.2: Dependent Variable measured on 4 occasions
Measure: MEASURE_1
Within-Subjects Factors
Time
Dependent Variable
1
Pre Training Score
2
Post Training1 Score
3
Post Training2 Score
4
Post Training3 Score
Figure 5.3: Descriptive Statistics of the Dependent Variable measured on 4 occasions
Descriptive Statistics
Pre Training Score
Post Training Score
Post Training2 Score
Post Training Score
Figure 5.4: Test of Sphericity
Mauchly's Test of Sphericity"
Measure: MEASURE 1
Mean
Std. Deviation
N
5.010
81438
200
6755
95894
200
7.240
86959
200
7.930
79893
200
Epsilon
Within Subjects
Effect
Mauchly's W
Approx. Chi-
Square
df
Sig
Greenhouse Geisser Huynh-Feld
Lower
bound
Time
878
6.252
5
104
.891
923
500
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional
to an identity matrix.
a. Design: Intercept
Within Subjects Design: Time
b. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the
Tests of Within Subjects Effects table.

Statistics that allow for inferences or estimates about the population. Inferential statistics enable analysts come to conclusions about the population based on sample data. Inferential statistics cover the basics of inferential statistics, all kinds of hypotheses tests and their confidence intervals, design of experiments, and statistical power and errors. It also includes point estimation techniques, limit theorems, sampling distributions, approximations, and bounds. Correlation, regression, and association are also covered under inferential statistics to infer relationships between variables.

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