**D2.1 Working with Variables.**

According to Morgan et al., “Measurement is an assignment of numbers or symbols to the different characteristics of variables according to rules. In order to under your variables, it is important to know their level of measurement”. These traditional terms as different from SPSS programs, sometimes they are not always the most useful for determining what statistics to use. Nominal variable is considered the most basic of lowest level of measurement, in which the numerals assigned to each category stand for the name of the category, but they have no implied order of value. In regard to dichotomous variables, it always has only two levels or categories. In some instances, they do have particular orders, in other instances they don’t. In ordinal measurement, they are not only mutually exclusive categories as in nominal scales, but the categories are ordered from low to high. While approximately normally distributed variables not only have levels or scores that are ordered from low to high, the frequencies of the scores are approximately normally distributed. It is important to distinguish between interval and ratio data because, interval ordered levels, in which the difference between levels equal, but no true zero, while ratio ordered levels; the difference between levels is equal, and there is a true zero.

**D2.2 z scores and the population.**

All normal curves can be converted into standard normal curves by setting the mean equal to zero and the standard deviation to one. A Z-score is a score which indicates how many standard deviations an observation is from the mean of the distribution. According to Bradshaw “Z-scores tend to be used mainly in the context of the normal curve, and their interpretation based on the standard normal table. It would be erroneous to conclude, however, that Z-scores are limited to distributions that approximate the normal curve”. Z-scores tell us how far a value is from the mean. When you standardize a variable, its mean becomes zero and its standard deviation becomes one. Thus, a Z score of -3 tells us that the value is -3 away from the mean. Based on the data the percentage of the scores between z of -2 and z of +2 is 95%.

**D2.3 Interpreting Output 4.1b.**

Based on the descriptive and the output for Variables Initially Labeled as Scale, it can be interpreted that the competence scale skewness statistic is more than 1.00 or less than -1.00. Skewness can be quantified to define the extent to which a distribution differs from a normal distribution. Thus, with the competence scale being skewed, we can deduce that it is not normally distributed. Based on the boxplot, there are four outliers, which include is 4, 10, 5 and 6. There is correlation between data.

**D2.4 Interpreting Output 4.4.**

Based on the data there are 75 participants all together, and based on the valid N, all 75 participants have data in each category. Based on the mean, 55% of the participants are female, thus leaving 45% as male. Over half of the participants were female in this study. The means shows the percentage or average of the participants. We can deduce 79% of the participants took algebra 1 in high school, while only 47% took algebra 2 in high school, with an average of 63% taking some type of algebra in high school. We can go on an deduce that 48% took geometry, while 27% took trigonometry, and 11% took calculus in high school.

References

Bradshaw. (n.d.). Retrieved January 23, 2019, from http://www.daylight.com/meetings/emug97/Bradshaw/Significant_Similarity/Z-scores.html

Morgan, G. A., Leech, N. L., Gloeckner, G. W., & Barrett, K. C. (2013). IBM SPSS for introductory statistics: Use and interpretation(5th ed.). New York: Brunner-Routledge.