# Statistics assignment

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Q1. A distribution that has much less variability around the mean score than a normal distribution called a Leptokurtic distribution. The distribution is leptokurtic because it is peaked more than a standard normal distribution curve, and it also has positive excess kurtosis. It has a tall, slender peak in the distribution. It has more values close to the mean. In the real life application, an investment can be a leptokurtic in that the risks in the returns come from the outlier events. This can be a stock for investors who are ready to take extreme risks.

Q2. A researcher designs a study to examine the effects of social skills training on a sample of middle school students. He also intends to examine the effects of the training separately for girls and boys. What role does the gender variable play in this research design?

IV– Assigned subject variable, in the example gender is an independent variable and is an assigned subject variable. It shows an example of performing multiple experiments at the same time. It is a two experiment each having different hypothesis and variables running concurrently. The researcher intends to find out the effect of training the students on life skills when the students are together and another study when the students are trained as per their gender.

Q3. Key test validity issues include:

Interpretability and usefulness of test scores are the key test validity issues. The evidence in the results should be easy to interpret; the evidence accumulated should support specific interpretation of the test results.

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The test results should be used for several purposes. Several factors can influence the valid and useful interpretations of the test scores. These factors include; i. Psychometric factors e.g. reliability, standard error of measurement, norms and validity of the instrument.

ii. Test taker factors i.e. the test takers membership and how the members can influence the results.

iii. Contextual factors; the relationship of the test to the instructional program opportunity to learn.

Statistics

Visualization test SAT math Competence Mosaic pattern

N Valid 75 75 73 75

Mean 5.2433 490.53 3.2945 27.413

Median 4.7500 490.00 3.5000 27.000

Std. Deviation 3.91203 94.553 .66450 9.5738

Skewness .536 .128 -1.634 .529

Kurtosis -.998 .943 3.037 2.106

Range 15.00 480 3.00 60.0

Q4. Please use the table to answer this question.

Which variable best approximates a normal distribution and which variable is least normal?

Most normal is SAT Math; least normal is competence the SAT Math has the most normal distribution and competence is the least normal. SAT math is the most normal distribution since its mean and median are close at 490.53 and 490.00 respectively and their values are high. Competence is least normal since the values of the mean and median are the least and it also has negative skewness.

Q5. Define and give an example of each of the following concepts: (two sentences)

1. Mediating effect- represents the indirect effect of IV on DV.

The mediating effect tends to identify and explain the process that constitutes the relationship between independent variables and the dependent variable by including a third variable i.e. the mediator variable. In the mediating model, the independent variable influences the mediator variable that later influences the dependent variable.

2. Construct validity- the degree to which a test measures what it claims to be measuring.

For example if a design is to measure whether educational program can increase the artistic ability amongst the pre-scholars, the construct validity will measure the measure of whether the research measures the artistic ability.

3. Sampled population- a subset of units of the population.

It is the collection of all the possible observation chosen from a sample. For example a poll taken to determine the number of people who will vote for a certain candidate, the total population is the number of all registered voters but the sampled population may be the voters who could be reached via phone calls only.

4. Latent variable- variables that are not directly observed but are rather inferred.

It may refer to the physical reality that can be measured principally but may not be for practical reasons. They only help reduce the dimensionality of data.

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