20211202061330discussion_board_questions

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Feb 20, 2024

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1 2 Peer Replies and discussion Board Questions Name: Class Title: Date: Discussion Forum Number:

2 Discussion Board Questions D4.5.1 Comparing and contrasting a between-groups design and a within-subjects design In a between-groups design, every study participant is only in one group or condition while in a within-subjects design there is a likely participant connection in the independent variable levels or conditions to the other independent variable levels or conditions (Morgan et al., 2020). Also, in a between-groups design, different participants will be testing every condition to expose every participant to a single user interface while in a within-subjects design, the same participant will test all the user interfaces or conditions (Raluca, 2018). D4.5.2. The information about variables, levels, and design one should keep in mind in order to choose an appropriate statistic For one to choose an appropriate statistic, the number of variables should be checked in the research hypothesis or question. If the variables are two, a bivariate statistic can be used and if the variables are three or more, the complex statistic can be used (Morgan et al., 2020). For levels and design, if an independent variable has two levels and it is a between-groups design, an independent samples t test is deemed to be ideal while for a within-subjects design we choose paired samples t test (Morgan et al., 2020). On the other hand, if the independent variable has 3 or more levels and it is a between-groups design, we choose one-way anova while if it a within- subjects design, we use GLM repeated measures anova as a statistical analysis option. D4.5.3. An example and explanation of a study where a researcher could appropriately choose two different statistics to examine the relations between the same variables Research problem: Effect of salt addition on growth and survival of a plant. The variables in this study example consist of amount of added salt, growth, and survival. The added salt is the independent variable while growth and survival are dependent variables. Salt addition

3 seems to affect both growth and survival of a plant and that is why the variable is considered independent while the latter are considered dependent. Growth is measured in height difference (scale) while survival is considered dichotomous (died=0 and survived =1). Also, salt amount is measured in milligrams per liter of water and it can be considered to be a scale variable. The hypotheses from the study example: the first one is ‘Salt addition makes the plant to grow’. The other hypothesis is ‘Salt addition makes the plant to die’. In this study, the researcher can choose two different statistics. For instance, in the first hypothesis one can use both descriptive and inferential statistic and since they are scale variables and there are repeated measures, the paired samples t test can be appropriate too. D4.5.6. Explanation of a statistic one would use if they wanted to see if there was a difference between three ethnic groups on math achievement One-way anova test is the statistic to be used. This is a basic difference research question according to Morgan et al., (2020) and math achievement variable has many levels while ethnic groups are three leveled. Math achievement is considered the dependent variable while ethnic group is the independent variable. Also, independent variable has three values, the design is between groups, and the dependent variable is a scale variable. D4.5.8. A statistic one would you use if they had one independent variable and one dependent variable The Chi-Square statistic will be used. The independent variable has 4 values (North, South, East, West), the design is between groups, and the dependent variable is dichotomous (Morgan et al., 2020). The statistic will try to scrutinize the differences between groups and if the variables are independent from the other.

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4 D4.5.9. A statistic one would use if they had three normally distributed (scale) independent variables plus one dichotomous independent variable one dependent variable (positive self- image), which is normally distributed We can use multiple regression statistic. The dependent variable is normal while there are two category independent variables (three normal and one dichotomous) which are mixed (between and within). The statistic is ideal because it can predict the positive self-image variable from multiple independent variables ( Weisburd et al., 2021 ). The statistical analysis will provide explanation for the dependent variable from more than two independent variables.

5 References Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020 ). IBM SPSS forintroductory statistics: Use and interpretation (6th Ed.). Routledge. Raluca, B. (2018). Between-subjects vs. Within-subjects study design. Retrieved from: https://www.nngroup.com/articles/between-within-subjects/ Weisburd, D., Wilson, D. B., Wooditch, A., & Britt, C. (2021). Multiple regression. In Advanced Statistics in Criminology and Criminal Justice (pp. 15-72). Springer, Cham.

6 Peer Reply 1: Descriptive Statistics, Ordinal Scale and Dichotomous Variable D3. 4.1. Output 4.1a and 4.1b The student states that the mean visualization test score is 5.2433 which is in agreement with my finding. The student attached a photo showing that there is a positive skewness of 0.044 for the math achievement test , and the minimum mosaic pattern test of -4.0 agreed which agrees with my findings. The positive skewness is a good sign since it shows that many students passed ( Makino & Chan, 2017 ). The student states that the variable is not quite skewed with the low skewness of 0.044 hence normal inferential statistics can be used and this is in agreement with my findings. Also, the student notes that the negative score is supposed to represent the lowest individual score and this is an area of improvement I should take note of as I had assumed there is no negative value of mosaic pattern test and saw it as an error. D3. 4.2. Using Output 4.1b The student notes that the competence scale has a skewness statistic of more than 1 and less than -1 which means that it is highly skewed and this is in agreement with my findings. Also, the student records that it is likely to be an ordinal variable which is an area I should improve on since the assumption might be true. The student states that the boxplot’s competence scale has three outliers which I am in disagreement since it is clearly four outliers. Also, the student records that the outliers show that the data is skewed which is not in agreement with my findings. However, the students add that the size of outliers determines if the data is skewed or not ( Makino & Chan, 2017 ). D3. 4.3. Using Output 4.2b The student posted that 4 participants have missing data and 94.7% of students have a valid motivation scale or competence scale score which is in agreement with my findings. Also,

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7 the student post shows that it is possible to tell how many are missing both motivation scale and competence scale scores which I disagree with. Morgan et al. (2019) shows that the N statistic in Output 4.1 is for the single variable and not both, while Valid N in Output 4.2b Case Processing table indicates all the cases that have missing data on at least one variable. D3. 4.4. Using Output 4.4 The student’s post is in agreement with my post that it is possible to interpret the means and goes ahead to give instances of how to express the mean as a percentage. The student states that 94.7% of students have a valid motivation scale or competence scale score and this is in disagreement with my findings and I think the student misinterpreted the question, not giving the rightful answer of the number of participants as 75. However, the student post states that 75 students have complete data and this is in agreement. The student post states that 45.3% are in the fast track and 100% took algebra 1 in h.s. which is not correct since Morgan et al. (2019) states that 45% are on the fast track and 79% took algebra 1 in h.s . D3. 4.5. Using Output 4.5 The student is in agreement with my post that 9.6% represents the percentage of students who responded to this question and identified as only Asian-American. Also, the student post agrees that 8% of students have visualization 2 scores of 6 while 66.7% have scores of 6 or less and it corresponds what Morgan et al. (2019) indicates on the results tables .

8 References Makino, S., & Chan, C. M. (2017). Skew and heavy‐tail effects on firm performance. Strategic Management Journal , 38 (8), 1721-1740. Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2019). IBM SPSS for Introductory Statistics: Use and Interpretation: Use and Interpretation . Routledge.

9 Peer Reply 2: Variables, Z Scores, Population and Output D2.3.1 Categorical Ordered Data The student states that categorical ordered data will be considered ordinal and it is in agreement with my findings. Just like in my post, the student goes ahead to note how Morgan et al. (2020) details that ordinal data is ordered and usually includes three or four levels. To label variables as ordinal, the student goes ahead to note that the level of magnitude between adjacent categories is uneven whereby the difference between low and middle income would probably not be the same as between middle income and high income. I would consider this to be an area of improvement since I did not go into detail as the student posted. D2.3.2 Types of Variables The student post starts by giving an overview of the types of variables which my post did not cover and should be an area of improvement in the next post when answering a question of this manner. When comparing and contrasting, the student considers the wide perspective of every variable whereas in my post I had only mentioned the unique features that makes a variable considered as nominal, dichotomous, ordinal, or normal. Morgan et al. (2020) suggests that it is worth considering the dichotomous variable as a special case of the normal variable and has two ordered or unordered categories as the student post states and this is in agreement with my findings. Also, the student post states that when a frequency distribution is obviously not normal, one should consider the variables to be ordinal, which is also a place of improvement I should consider since I did not go into that detail. According to Morgan et al. (2020), normal variables should have at least five ordered categories feature continuous data and may or may not have a true zero and this is in agreement with my post. We are in agreement that the difference between interval and ratio variables is that ratio variables have a true zero and are less applicable

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10 in social science research (Morgan et al., 2020). The explanation provided by the student is quite detailed by stating that the inclusion of true zero would imply values such as no intelligence, no emotion or no attitude. This means I should improve on that by doing more research concerning the question. D2.3.3 Normal Distribution The student post is in agreement that 34% of the area under the standard normal curve is within one standard deviation above and one standard deviation below the mean as detailed by Morgan et al. (2020). The student goes on to explain what the other area under the curve represents and it should be an area of improvement in the next post. There is a decreased likeliness of occurrence when the score is more than one standard deviation away from the mean. Therefore, similar to the student post, 32 percent of scores are more than one standard deviation from the mean in a normal distribution. D2.3.4 Z Scores The student states that normal frequency distribution can be described using Z scores. An interesting fact the student says is that the normal distribution where the mean has a value of zero and the standard deviation has a value of one and this can be confirmed by Mishra et al. (2019) . From the student’s perspective that the z score enables one to compare different normal distributions by converting the raw data into the standard normal distribution, it is also important to note that a zero Z score denotes exactly average values while a more than 3 score denotes that the value is greater than average. Therefore, it is true that 99 percent of the area under the normal curve is within three standard deviations above and below the mean. The student post also agrees with mine that 95 percent of scores are between a z score of -2 and +2. Morgan et al. (2020) states that it is important because it is where the statistical significance is defined.

11 D2.3.5 Displaying Nominal Data The student agrees with my post that a frequency polygon is for continuous data while nominal data is non continuous hence will not be represented that well (Morgan et al., 2020). Also, the student states that a bar chart could be a better option but goes ahead to dispute the claim saying that there will be lack of order with the bars not touching which is in agreement with my findings. However, my post added a pie chart as a better option for displaying nominal data.

12 References Mishra, P., Pandey, C. M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Annals of cardiac anaesthesia , 22 (1), 67. Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020 ). IBM SPSS for introductory statistics: Use and interpretation (6th Ed.). Routledge.

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