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Methods and Analysis of Quantitative Research | R7031 BLE

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Research Scenario

            An organization wants to determine if parents with different number of children differ on the overall satisfaction in June with free after school day care programs. The firm collected demographic information of parents: percentage of the school program the child is in day care programs, type of student, whether the child receives free lunch program, and number of children the parent has in school.

            The over satisfaction as well as satisfaction with education activities, safety, physical activities, social activities, and day care program is measured on a scale of one to 10.

Code book     

VariablePositionLabelMeasurement Level 
id1IDScaleParticipant ID number
Safety2Safety of ChildrenScaleOn a scale of 1 to 10, how would you rate the safety of the environment for the children?
Education3Educational ActivitiesScaleOn a scale of 1 to 10, how would you rate your satisfaction with the educational activities?
Social4Social ActivitiesScaleOn a scale of 1 to 10, how would you rate your satisfaction with the social activities?
Physical5Physical ActivitiesScaleOn a scale of 1 to 10, how would you rate your satisfaction with the physical activities (sports, dance, etc.)?
Newstudent6Type of StudentOrdinal0 = new student 1 = returning student
Usage7Usage LevelScaleWhat percent of the school semester is your child in the day care program?
Osatjan8Overall Satisfaction in JanuaryScaleOn a scale of 1 to 7, rate your overall satisfaction with the day care program.
Osatjun9Overall Satisfaction in JuneScaleOn a scale of 1 to 7, rate your overall satisfaction with the day care program.
Title110Receives Title 1 Free LunchNominalDoes your child receive a free lunch? 0 = No; 1 = Yes
Family11Number of ParentsNominal0 = One Parent/Guardian; 1 = 2 Parents/Guardians
Children12Number of Children in SchoolNominal1 = One Child; 2 = Two Children; 3 = Three or more

Variables in the working file

Problem background           

The district education department is interested in determining the effectiveness of free after school day care program in the district. This will help the district to determine whether to continue creating awareness of the free after school day programs. This will also help the county officials has achieved what they declared in their manifesto. The district officials claims that the distribution of the number of children in school is not consistent, the overall satisfaction in June is different between free lunch program, the overall satisfaction in June is difference between the number of children in school, and the free lunch program and number of children in school have an in interactive effect on the overall satisfaction in June. The health department recruited an analytical firm to test these claims.

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Problem statement   

The purpose of this study is to examine whether there is statistical significant difference in the overall satisfaction with free after school day care programs on the number of children a parent has in school. The study also investigates the effect of free lunch program (yes/no) and children (number of children in school) on the overall satisfaction with free after school day care programs. The study also examines whether the overall satisfaction with free after school day care program differs based on free lunch program. Finally the study will examine whether the distribution of children (number of children 9in school) differ from what one would expect by chance.

Table 1: Frequency distribution of Free Lunch program

Receives Title 1 Free Lunch
 FrequencyPercentValid PercentCumulative Percent
ValidNo2652.052.052.0
Yes2448.048.0100.0
Total50100.0100.0 

            Majority of the children receive free lunch in after school day care programs. This is shown also in the bar charts by the longest bar.

Table 2: Frequency distribution of Free Lunch program

Number of Parents
 FrequencyPercentValid PercentCumulative Percent
ValidOne Parent/Guardian2448.048.048.0
Two Parents/Guardians2652.052.0100.0
Total50100.0100.0 

            Children with two parents are many in the study sample. This is shown by the frequency table as well as the bar chart.

Table 3: Frequency distribution of Number of Children in School

Number of Children in School
 FrequencyPercentValid PercentCumulative Percent
ValidOne Child1836.036.036.0
Two Children1836.036.072.0
Three or More Children1428.028.0100.0
Total50100.0100.0 

            Parents with one child and two children in schools is greater than parents with three r more children. The longest bars represent parents with one child and two children.

Table 4: Frequency distribution of family Size

Family Size
 FrequencyPercentValid PercentCumulative Percent
ValidOne Child1836.036.036.0
Two Children1836.036.072.0
Three or More Children1428.028.0100.0
Total50100.0100.0 

            Parents with one child and two children is significantly higher than parents with three or more children.

Table 5: Descriptive statistics

Descriptive Statistics
 NMinimumMaximumMeanStd. DeviationVarianceSkewnessKurtosis
StatisticStatisticStatisticStatisticStatisticStatisticStatisticStd. ErrorStatisticStd. Error
Safety of Children501.07.04.3401.67342.800-.376.337-.287.662
Educational Activities503.08.05.3401.15371.331-.048.337.321.662
Social Activities501.05.02.880.8953.802-.112.337-.221.662
Physcial Activities501.05.02.660.8478.719.101.337.372.662
Usage Level5025.065.044.6009.095982.735.028.337-.485.662
Overall Satisfaction in January501.007.003.58001.371581.881.320.337.217.662
Overall Satisfaction in June503.07.04.700.9530.908.206.337-.546.662
Valid N (listwise)50         

            The average overall satisfaction in June (M=3.58) is greater than the average overall satisfaction in January (M=4.700). The average overall satisfaction with education activities in after school day care programs is greater than the overall satisfaction with social activities (2.880), safety of children (M=4.3400), and physical activities (M=2.660).

Table 6: Frequency distribution of Safety of children.

Safety of Children
 FrequencyPercentValid PercentCumulative Percent
Valid1.0510.010.010.0
2.012.02.012.0
3.0714.014.026.0
4.01428.028.054.0
5.01020.020.074.0
6.0816.016.090.0
7.0510.010.0100.0
Total50100.0100.0 

Table 6: Frequency distribution of Educational Activities.

Educational Activities
 FrequencyPercentValid PercentCumulative Percent
Valid3.048.08.08.0
4.0510.010.018.0
5.01938.038.056.0
6.01632.032.088.0
7.048.08.096.0
8.024.04.0100.0
Total50100.0100.0 

Table 7: Frequency distribution of Social Activities.

Social Activities
 FrequencyPercentValid PercentCumulative Percent
Valid1.036.06.06.0
2.01326.026.032.0
3.02244.044.076.0
4.01122.022.098.0
5.012.02.0100.0
Total50100.0100.0 

Table 7: Frequency distribution of Physical Activities.

Physcial Activities
 FrequencyPercentValid PercentCumulative Percent
Valid1.048.08.08.0
2.01632.032.040.0
3.02448.048.088.0
4.0510.010.098.0
5.012.02.0100.0
Total50100.0100.0 

Table 8: Frequency distribution of Usage level.

Usage Level
 FrequencyPercentValid PercentCumulative Percent
Valid25.012.02.02.0
28.012.02.04.0
29.012.02.06.0
31.012.02.08.0
32.012.02.010.0
34.012.02.012.0
35.024.04.016.0
36.024.04.020.0
38.036.06.026.0
39.048.08.034.0
41.036.06.040.0
42.024.04.044.0
43.024.04.048.0
44.012.02.050.0
45.012.02.052.0
46.012.02.054.0
47.036.06.060.0
48.024.04.064.0
49.0510.010.074.0
50.012.02.076.0
51.012.02.078.0
53.012.02.080.0
54.036.06.086.0
56.012.02.088.0
57.012.02.090.0
58.024.04.094.0
59.012.02.096.0
60.012.02.098.0
65.012.02.0100.0
Total50100.0100.0 

Table 9: Frequency distribution of Overall Satisfaction in January.

Overall Satisfaction in January
 FrequencyPercentValid PercentCumulative Percent
Valid1.0036.06.06.0
2.00714.014.020.0
3.001530.030.050.0
4.001326.026.076.0
5.00918.018.094.0
6.0012.02.096.0
7.0024.04.0100.0
Total50100.0100.0 

Table 10: Frequency distribution of Overall Satisfaction in June.

Overall Satisfaction in June
 FrequencyPercentValid PercentCumulative Percent
Valid3.048.08.08.0
4.01938.038.046.0
5.01632.032.078.0
6.01020.020.098.0
7.012.02.0100.0
Total50100.0100.0 

            The graphs above have bell shaped superimposed curve indicating that the data is normally distributed. This is one of the basic assumptions for ANOVA, Independent T-test, and two way ANOVA among others.

Table 11: Correlation analysis

Correlations
 Safety of ChildrenEducational ActivitiesSocial ActivitiesPhyscial ActivitiesUsage LevelOverall Satisfaction in JanuaryOverall Satisfaction in June
Safety of ChildrenPearson Correlation1.193.436**.112.662**.206.628**
Sig. (2-tailed) .180.002.439.000.152.000
N50505050505050
Educational ActivitiesPearson Correlation.1931.317*.726**.338*.195.484**
Sig. (2-tailed).180 .025.000.016.174.000
N50505050505050
Social ActivitiesPearson Correlation.436**.317*1.133.658**.340*.555**
Sig. (2-tailed).002.025 .356.000.016.000
N50505050505050
Physcial ActivitiesPearson Correlation.112.726**.1331.257.173.326*
Sig. (2-tailed).439.000.356 .071.229.021
N50505050505050
Usage LevelPearson Correlation.662**.338*.658**.2571.384**.753**
Sig. (2-tailed).000.016.000.071 .006.000
N50505050505050
Overall Satisfaction in JanuaryPearson Correlation.206.195.340*.173.384**1.479**
Sig. (2-tailed).152.174.016.229.006 .000
N50505050505050
Overall Satisfaction in JunePearson Correlation.628**.484**.555**.326*.753**.479**1
Sig. (2-tailed).000.000.000.021.000.000 
N50505050505050
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).

            There is a strong statistical significant correlation between the overall satisfaction in June and safety of children (P=0.000, r=0.628). There is a very strong positive correlation between the overall satisfaction in June and usage level (P=0.000, r=0.753). There is a weak positive correlation between the Overall satisfaction in January and Physical activities, which is not significant (P=0.229, r=0.173). There is a weak positive correlation between There is a weak positive correlation between safety of children and overall satisfaction with educational activities, which is not statistical significant (P=0.180, r=0.193). There is a moderate correlation between overall satisfaction with social activities and physical activities, which is not statistical significant (P=0.356, r=0.133). All the analysis for this study are conducted at 0.05 level of significance.

Question 1

The study also examines whether the overall satisfaction in June with free after school day care program differs based on free lunch program.

Null Hypothesis

            On average, there is no statistical significant difference in the overall satisfaction in June based on whether a child receive free lunch.

Alternative Hypothesis

            On average, there is statistical significant difference in the overall satisfaction in June based on whether a child receives free lunch.

            The appropriate test for hypothesis is Independent T test. There are two categorical variables (Free lunch) and one continuous variable (Overall satisfaction in June). The previous steps performed on the data indicate that overall satisfaction in June is normally distributed and there are no significant outliers. Stem and leaf plot is used to show possible outliers which are then removed accordingly.

Independent Samples Test
 Levene’s Test for Equality of Variancest-test for Equality of Means
FSig.TdfSig. (2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the Difference
LowerUpper
Overall Satisfaction in JuneEqual variances assumed.066.798.21147.834.0550.2605-.4691.5791
Equal variances not assumed  .21146.786.834.0550.2607-.4695.5795

            The levene’s test show that the data assumed equal variance (P>0.05). There is no statistical significant difference on the overall satisfaction in June based on whether the child receives free lunch.

Question 3

Is there a statistical significant difference in the overall satisfaction with free after school day care programs on the number of children a parent has in school.

Null Hypothesis

            On average, the overall satisfaction in June is the same among the number of children a parent has in school.

Alternative Hypothesis

On average, the overall satisfaction in June is not the same among the number of children a parent has in school.

            The appropriate test for this analysis is one way analysis of variance. There is more than two treatments (one child, two children and three or more children). The overall satisfaction in June is dependent variable. The test for normality and outliers has already been performed as indicated above (Warner, 2013). The possible outliers are removed accordingly. The test is performed at 0.05 level of significance.

ANOVA
Overall Satisfaction in June
 Sum of SquaresDfMean SquareFSig.
Between Groups23.816211.90835.833.000
Within Groups15.28646.332  
Total39.10248   
Multiple Comparisons
Dependent Variable: Overall Satisfaction in June  Tukey HSD
(I) Number of Children in School(J) Number of Children in SchoolMean Difference (I-J)Std. ErrorSig.95% Confidence Interval
Lower BoundUpper Bound
One ChildTwo Children-1.1667*.1922.000-1.632-.701
Three or More Children-1.6838*.2098.000-2.192-1.176
Two ChildrenOne Child1.1667*.1922.000.7011.632
Three or More Children-.5171*.2098.045-1.025-.009
Three or More ChildrenOne Child1.6838*.2098.0001.1762.192
Two Children.5171*.2098.045.0091.025
*. The mean difference is significant at the 0.05 level.

            The ANOVA output indicate that there is a statistical significant difference on the overall satisfaction among the number of children parents have in after school day care programs (P<0.05). The multiple comparison table is used to show whether the differences is. As it can be seen, the difference exist between any possible combination (P<0.05).

Question 4

What are the effects the effect of free lunch program (yes/no) and children (number of children in school) on the overall satisfaction with free after school day care programs.

Null Hypothesis

            The population means for free lunch program are equal.

Alternative Hypothesis

            The population means for free lunch program is different.

Null Hypothesis

            The population means for the number of children in school is equal.

Alternative Hypothesis

            The population means for the number of children in school is not equal.

Null Hypothesis

            There is possible interaction between free lunch program and number of children in school.

Alternative Hypothesis

            There is no interaction between free lunch program and number of children in school.

            The appropriate test for the hypothesis is two way analysis of variance. The assumptions for normality and significant outliers is already performed as shown by the previous analyses in this study and the possible outliers removed accordingly.

Tests of Between-Subjects Effects
Dependent Variable: Overall Satisfaction in June
SourceType III Sum of SquaresDfMean SquareFSig.
Corrected Model24.323a54.86514.153.000
Intercept933.2011933.2012715.095.000
Children22.854211.42733.247.000
Title1.1861.186.540.466
Children * Title1.2762.138.402.672
Error14.77943.344  
Total1100.00049   
Corrected Total39.10248   
a. R Squared = .622 (Adjusted R Squared = .578)

            The P-value in children row indicate the null hypothesis is not accepted, and conclude that the overall satisfaction based on the number of children a parent have in school is not the same (P<0.05). The P-value of the Title row is greater than the level significance. This implies that the null hypothesis is not rejected and conclude that there is no statistical significant difference on overall satisfaction in June based on free lunch program (P>0.05). The children*Title 1 row shows that there is statistical significant interaction.

Question 8

Finally the study will examine whether the distribution on number of children (1 child, 2 children and 3 children) differ from what one would expect by chance.

Null Hypothesis

            The distribution on number of children is consistent from what one would expect by chance.

Alternative Hypothesis

            The distribution on number of children is not consistent from what one would expect by chance.

            The appropriate test is Chi square goodness of fit. The data is mutually exclusive. It consist of three groups (one child, two children, three or more children). Second, there is no relationship between the participants. Finally, there is at least 5 expected frequencies in each group of the categorical variable (one child, two children, three or more children). This is shown in the SPSS output. This are the basic assumption for chi square goodness of fit,

Number of Children in School
 Observed NExpected NResidual
One Child1816.31.7
Two Children1816.31.7
Three or More Children1316.3-3.3
Total49  

            The above table show the expected frequencies if the null hypothesis is proved to be right.

Test Statistics
 Number of Children in School
Chi-Square1.020a
Df2
Asymp. Sig..600

            The test statistics table shows that the null hypothesis is not rejected (P>0.05). This implies that the distribution on number of children is consistent from what one would expect by chance.

Conclusion

            The findings above shows that the distribution of the proportion of the number of children (one child, two children, three or more children) is consistent. This implies the proportion is what one could expect by chance. The findings also suggest that there is no difference on the overall satisfaction in June between parents whose children receive free lunch and those who don’t receive free lunch. Free lunch program and number of children in school have an interactive effect on the overall satisfaction in June. Additionally, there significant difference on the overall satisfaction based on the number of children a parent has in school.

Reference

Warner, R. (2013). Applied statistics (1st ed., pp. 23-25). Thousand Oaks, Calif.: SAGE Publications.