04- Z scores
Slide 1: Hello! I hope this powerpoint finds you well. I realize that this is a rigorous course and that you may be feeling discomfort as you navigate new terms and concepts. In practice courses, brain will recall concepts that are familiar making new learning experiences less anxiety-provoking. However, when learning research and statistics few students have little memory of previous learning of this topic to reduce discomfort. That said, it is important for you to recognize and appreciate your growth during this course as well as to balance your activities. Being an online student, I imagine that you are very busy assuming many roles. Therefore, I suggest that you engage in a pleasurable activity at least every day – for
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Slide 3: A Z-score informs us if a variable’s score or value is equal, below, or above the mean. It also determines the exact proportion or percentage of scores that fall between any two scores of normally distributed scores. This sounds similar to the standard deviation; however, standard deviations are set values that fall on a distribution; whereas, Z-scores or values may lie anywhere on the normally distributed curve. Hold that thought and I will go into greater detail as we progress.
Slide 4. The following is a good guideline to understand Z scores and their relationship to standard deviations.
Slide 5: Let’s look at a normal curve, using Z scores. On the left, we see a distribution title Positive Z. Look at the highlighted area, B, which represents the percentage of scores or values between the mean and a particular Z-score above the mean. This Z score represents a positive Z-score as it is to the right of the mean. Notice that the area to the left of the mean equals 50% of the scores or values of a variable. Remember we have symmetry of the curve on both sides or 50% of scores or values on both sides.
On the right, we see a normal curve with a highlighted area, B, which represents the percentage of scores or values between the mean and a particular Z-score below the mean. This represents a negative Z-score.
Slide 6: Before we move on, it might help you to learn the formula for obtaining a Z-score. A Z-score equals the raw score of a
This is a histogram were the tail goes to the right, it means the average is larger than the median.
The questions in this instrument are weighted a numerical value of zero to three, with three being the highest score on each question.
As discussed in the previous section, a normal distribution has particular characteristics it conforms to. i.e.
Standard deviation is a way of visualizing how spread out points of data are in a set. Using standard deviation helps to determine how rare or common an occurrence is. For example, data points falling within the boundaries of one standard deviation typically account for about 68% of data and those between (+/-)1 standard deviation and (+/-)2 standard deviations make about 27% combined. This can be better visualized by using a bell graph. Using the mean and standard deviation, the points where standard deviations occur can be drawn on the graph to better understand which data is rare and which is common.
The area under the curve to the left of the unknown quantity must be 0.7 (70%). So, we must first find the z value that cuts off an area of 0.7 in the left tail of standard normal distribution. Using the cumulative probability table, we see that z=0.53.
Standard deviation is important in comparing two different sets of data that has the same mean score. One standard deviation may be small (1.85), where the other standard deviation score could be quite large (10)(Rumsey,
(c) The mean of the sample and the value of Z with an area of 5% in the left tail.
The area under a normal curve with mu = 35 and sigma = 7 is 0, 1, or 2?
Slide 15: Here’s the same curve demonstrating the z-score values for 2.5% at each tail.
For children: the BMD is given as a Z score. It compares to the normal range for children of the same age. The Z score curves resembles growth chart curves. A Z score of 0 is similar to the middle line, a Z score of +2 is similar to the highest line and a Z score of -2 is similar to the lowest line. Z scores do not take into account the child’s height or body size.
In two normal distributions, the means are 100 for group I, and 115 for group II. Can an individual in group I have a higher score than the mean score for group II? Explain.
1. Why is a z score a standard score? Why can standard scores be used to compare scores from different distributions? It is a scores relationship to the mean indicating whether it is above or below the mean. It does this by converting scores to z score. Yes – keep going – just a bit more is needed.2 out of 3 pts
If the percent of sedans that gives more than 44 mpg is 0%, z-score is 4.33.
7. a) How are the scores reported? b) What kind of scores does the instrument yield?
The Z-score formula for predicting bankruptcy was published in 1968 by Edward I. Altman, who was, at the time, an Assistant Professor of Finance at New York University. The formula may be used to predict the probability that a firm will go into bankruptcy within two years. Z-scores are used to predict corporate defaults and an easy-to-calculate control measure for the financial distress status of companies in