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The Test for statistical significance

Psychology – Focus of the Final Exam          

Part 1Essay 1


The Test for statistical significance is used to address questions like, what probability exists between two variables and the probability of a chance occurrence. They indicate the probability of making an error where a relationship exists. A confirmation of a 100% relationship is not possible between variables. The sources of errors are many and they cannot be all possibly be controlled for example the problems with validity and reliability, sampling errors, simple mistakes and also researcher bias. By applying the probability theory and also the normal curve, the probability of being wrong can be estimated when an assumption of finding a relationship is true. But the statistical significance is not similar to practical significance.

Part 1Essay 2

The main purpose of correlation research is to determine the rate or degree of relationship that exists between one or several variables. Variables can basically relate to each other without causing the other one to occur.

The other purpose is to develop the prediction models in order to predict or forecast the future value of a particular variable from its current value of one or more variables. Common models of prediction are applied in the education sector to predict student’s college performance by using their admission exam scores. There are two types or categories of correlation figures in statistics: bivariate (has two variables) and multi-variate (has many variables). These coefficients are mostly used to satisfy the initial purposes as mentioned above, that’s to identify the basic strength and the direction of the relationship between variables while the multi-variables correlation statistics is used to generally support the next purpose that’s the second purpose which is to develop the prediction models.

A correlation that lies between the values 0.7 to 1 is considered to be positively strong. This means that the correlation of 0.75 that is the predictor between the IQ and the GPA is strong, that’s the GPA and the IQ strongly relate to one another. An increase in IQ leads to a direct increase in GPA levels. But to determine its effectiveness of how good the predictor is or if the college GPA and the IQ are good predictors, the figure 0.75 is squared which equals to 0.5625. This means that 56% of the variance in college GPA and IQ scores can be explained by the predictor. The remaining 44% is explained by the other variables.  If the IQ increases at the same rate as the GPA, then the relationship is directly related. Factors like education level and performance have an impact on the variables and they can influence the results of the correlation.

The sample size and the standard deviation are some of the factors that can affect the size of correlation. Regression analysis is required to predict GPA as there are other factors that also affect the GPA.

Variables can basically relate to each other without causing the other one to occur. The connection between Correlation and causation can be described by the following example. When the light switch is moved to a particular position, the lights are activated and they turn on but when the light switch is adjusted in the opposite direction the lights go off. The lights in a room cannot go off without turning the switch button. The switch can also be adjusted to the right direction and fail to light when there is no electricity. For someone who has no knowledge of electricity will be forgiven to imagine that adjusting the switch causes the lights to glow in the room. So a relationship exists between the light and the light switch but it’s not a causation-effect relationship but a correlation one.

To evaluate the correlation research findings a test of statistical significance should be carried out. The alpha (0.05) can be used to test the results. However, correlation is the best the best statistical inference for the data.

Part 1. Essay 2

The claim being investigated is that the nasal treatment of flu is more effective than the shot. The claim is that the nasal effectiveness is x ≥ 16% while the shot is x < 16%. One of the statements has to be a null hypothesis and the other one is an alternative hypothesis. The null hypothesis has the equality sign. For the problem above, the null hypothesis Ho: x = 16 it’s normal to use the equal sign for the null hypothesis and not the greater than or less than signs. The other statement that does not have the equality sign is the alternative hypothesis or H1: x < 16

Two or one Tail

The statement of the problem at hand determines the kind of test to be used. A two tailed test is chosen when the alternative hypothesis has an equal to sign and the one tailed test is used when the alternative hypothesis has a strict inequality. For this problem we will apply the one tailed test.

The kind of test statistic and distribution to use depends on how the population distribution to be used. If the bell curve is applied then the standard normal distribution is applicable and a table of the Z-scores will be used.

Which vaccine is  more effective in preventing flu
        Nasal Spray                      Shot Total
Developed Did notDevelopedDid notTested

The test statistics is calculated from the formula of the mean of the given sample and instead of the standard deviation the standard error of the mean is used. For these particular problem p = value method is applied.

The p-value method is used in this case, the p-value = 0.008 and the level of significance is 0.005.  The level of significance is less than the p-value we accept the null hypothesis.

Part 1. Essay 3

Lot 1                                                                 Lot 2

                     Section1  Section 2                            Section 1 Section 2     

 2.27.3 2.27.3
 2.57.6 2.57.6
 2.78.1 2.78.1
 2.98.2 2.98.2
 3.18.5 3.18.5
 3.59.2 3.59.2
 4.19.3 4.19.3
 4.39.5 4.39.5
 4.79.5 4.79.5
 4.815.2 4.815.2
Sum34.892.4 2.27.3
Mean3.489.24 2.57.6
Mode#N/A9.5 2.78.1
Stdev0.9413942.237161 2.98.2
Range2.67.9 3.18.5
Skew0.1902232.443916 3.59.2
Kurtosis-1.57096.86883 4.19.3

The first section has a population of 10 items (N= 10) with relative figures whose values are almost similar. The range is very small and the figures can easily be estimated. The second section has a very wide range which is 7.9 compared to 2.6 in the first section. The figures in the second section have an outlier which is almost one and half times the figure just below it. The outlier is 15.2 which widens the range.

An outlier affects the results of a set of data and they can mislead as for instance the mean for the second section in lot one and two is 9.24 while without the outlier it would be 8.58. The outlier interferes with the mean of the data and gives misleading results.

Some of the values changed while some like the average and the mode remained the same. The totals for the sum were 34.8 and 92.4 in the first lot. While in the second lot the totals were 69.6 and 184.8 respectively. The mean remained the same in the first lot. The mean for the first and the second lot were 3.48 and 9.24. The mode in the first lot was not applicable in the first part as all the figures appeared only once while in the second section it was 9.5 while the second lot was 2.2 and 9.5 respectively. The standard deviation in the first lot was 0.941394 and 2.237161 and 0.916285 and 2.177493 for the second lot respectively. The range also remained the same for the first and second lot. The skewness in the first lot was 0.190223 and 2.443916 while the second lot was 0.17372 and 2.231898 respectively. The kurtosis for the first lot was -1.5709 and 6.86883 and -1.49733 and 4.727574 respectively.

Part B

The sturdy

The effectiveness of introduction of solid food to infants at around six months of age


This is a research on the critical belief that is based on targets that seeks to promote and introduce solid foods to babies aged around six months. (Magarey, Battistutta, Nicholson, Farrell, Davidson, & Cleghorn, 2009) Mothers in their first pregnancies (N=375) were asked to fill a belief based questionnaire and later they were traced to fill up the second questionnaire confirming the age they introduced their babies to solid foods. The beliefs about the partners or spouses (β = 0.16) while the doctors recommendations (β = 0.22) and the other control beliefs that were based on commercial baby foods that fronted the introduction of solid foods before six months and (β =- 0.20) for introduction of baby foods at six months. Programs that seek to change some of the critical beliefs that are against the introduction of solid foods at around six months. Good nutrition is necessary and fundamental for the overall good growth and development of an infant and throughout life. The introduction of solid foods also known as weaning or complementary feeding in children who were previously fed on a continuous diet of mostly breast milk or formular. To achieve optimal growth, good health and development of infants the World Health Organization recommended exclusive breast feeding for infants for the first six months of their lives. (WHO, 2003) In most countries in the world recommend the same and the introduction of solid foods particularly at the age of four months or less is associated with negative health problems in infants may lead to renal or gastrointestinal problems. (Naylor & Morrow, 2001)

In 2008, a sturdy was conducted known as the Nourish trial. (Magarey, Battistutta, Nicholson, Farrell, Davidson, & Cleghorn, 2009). Mothers who were over 18 yrs and who had delivered healthy babies in Brisbane and Adelaide in Australia participated in the sturdy. The mothers had been approached earlier and had given their consent on participating in the nourish sturdy when they were still in the post natal wards. The mothers who consented formed the sampling frame of the sturdy. Under the separate ethics approval guidelines, each of mother was invited separately to fill the TPB forms that contained the questionnaires one or two months before they were enrolled on the nourish trial.


In the first instance 85% (N = 1932) of all the mothers who were eligible and were approached on the postnatal hospital wards, 74% (N = 1422) who gave out their contact details. Among those who never gave their contacts, 44% (N = 510) provided a brief demographic information like university education (41 Vs22%) There were other differences like ages of birth (27 Vs 26 yrs) and also differences in birth weights, 3.46 kgs and 3.48 kgs. Some 379 mothers were disqualified when their children turned three months before the commencement of the exercise. A total of 683 mothers received the questionnaires out of which 43% were in Adelaide while the remaining were in Queensland, Australia. Only 54% of those who returned the questionnaire were enrolled in the Nourish trial. The questionnaire concentrated on direct TPB predictors (these were subjective norms, attitudes & perceived behavioral control) Other indirect TPB predictors were also assessed by the questionnaire. The Nourish trial included two rounds of data collection. The first questionnaire (infants that were aged around 3 months) assessed the indirect and also the direct predictors on the TPB. The other one was a follow up questionnaire (when the infants reached around seven months) when the mothers introduced solids for the first time.

The mothers received invitation that explained the nature of the sturdy together with the questionnaire in an envelope that contained stamps for mailing back the response whether it was positive or negative. The mothers were kindly requested to return the questionnaire whether itwas filled or not. The approval for the nourish participation was obtained from the relevant hospital before the exercise begun.

The questionnaires were developed in accordance with the TPB methods that are recommended for such exercises. (Ajzen, 199) The 7-point likert scales ranged from extremely likely (7) to extremely unlikely (1) and they included the following options Behavioral, control belief and normative choices. The Pearson product moment correlation matrix was initially analyzed to identify the beliefs that directly correlated with the behavior of early introduction of solid foods.


According to the study, the beliefs have greater impact on the mother’s behavioral intentions than actually the actions themselves. The study included the quantitative examination of the normative and critical beliefs that mostly influence the mother’s decisions to wean infants when they have not attained the six months period. These beliefs stem from their spouses, doctors and other peer group influences. (Ajzen, 1991)


The overall result suggests that the normative beliefs that are acquired from the partners or spouses and doctors are very important when determining the introduction age for solid food intake in infants. The marketing messages on suitability of commercial infant food before the age of six months are also very influential. Based on the results obtained during the sturdy, strategies to encourage mothers to wean their children beginning at the age of six months should include anticipatory guidelines that include professionals and mostly doctors to support the mothers in delaying the introduction of complementary foods till the infants reach six years.

The strengths and limitations of the study

The study’s strengths are in the identification of a unique and a defined behavior in a sample that was widespread and diverse. The study received very strong support from diverse quarters and its results were created more awareness on the respective subject. The mothers who participated included highly educated women and also the average ones. The limitations were encountered are the self report data which may have included some bias mostly from the predominately Caucasian community who may have answered the questions on expectations and whose answers may not have been genuine. (Wright, Parkinson & Drewett, 2004)

The future additional forms of statistical analysis and research should include the efficacy of the normative and belief based framework and create a TPB that applies to mothers on their subsequent pregnancies and if their decisions are influenced by other factors besides the influence on doctors, family members and children commercials. (Terry, Hogg & White, 1999) To conduct a follow up study, a similar TPB that was initially used during the post natal questionnaire would be utilized first during the seventh month when most mothers have successfully weaned their children and have had the experience and seen the effects of early or later introduction of solid foods to their children. Later follow-ups would concentrate on their decisions whether to maintain their first experiences or adopt other alternatives. These is important as first time mothers are mostly more careful when handling their first born children but they may maintain the same standards in their subsequent deliveries. According to the study, most beliefs that have greater impact on the mother’s behavioral intentions actually come from other members of the family or other close friends. The study included the quantitative examination of the normative and critical beliefs that mostly influence the mother’s decisions to wean infants when they have not attained the six months period. These beliefs stem from their spouses, doctors and other peer group influences. All these sources of influence must also be considered when doing a follow up. Some of the positions that had been taken by certain parties change over time but their influence may still have the same effect on the same people only with a different kind of perception or view. The major lesson from these research finding is that most decision or the primary influence on most mothers are from their spouses and their doctors. For a complete change of mind, these two groups should be included in making policy changes or strategies that touch on infant’s health.


These study provides information on the TPB belief based concept and which can be utilized to form the requisite strategies that would influence mothers’ decisions to delay the weaning age at least until the infants are aged six months and probably over and also to promote exclusive breast feeding during the initial six months period.


Ajzen, I. (1991). The theory of planned behavior, Organizational Behavior and Human

Decision Processes, 50(2), 179-211

Magarey, D.L., Battistutta, D., Nicholson, J. M., Farrell, A., Davidson, G., & Cleghorn, G. (2009). The NOURISH randomized control trial: Positive feeding practices and food preferences in early childhood – a primary prevention program for childhood obesity. BMC Public Health 9, 387

Terry, D. J., Hogg, M. A., & White, K. M. (1999). The theory of planned behaviour: Self-identity, social identity and group norms. British Journal of Social Psychology, 38(3), 225-244

World Health Organization, (2003). Global strategy for infant and young child feeding, Geneva: WHO.

Wright, C. M., Parkinson, K. N., & Drewett, R. F. (2004). Why are babies weaned early?

Data from a prospective population based cohort study. Archives of Disease in Childhood, 89

(9), 813-816.

Naylor, A. J., & Morrow, A. L. (2001). Developmental readiness of normal full term infants

to progress from exclusive breastfeeding to the introduction of complementary foods:

Reviews of the relevant literature concerning infant immunologic, gastrointestinal, oral motor and maternal reproductive and lactation development. Washington D.C: Wellstart International and the LINKAGES Project Academy for Educational Development

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