Statistics for Data Analyst - Statistics MCQs, Analysis, Software

MCQs Introductory Statistics 3

Dec 3, 2024May 1, 2019 by Muhammad Imdad Ullah

Post Views: 79

The post is about MCQs Introductory Statistics. There are 25 multiple-choice questions covering topics related to the measure of dispersions, measure of central tendency, and mean deviation. Let us start with the MCQs introductory statistics quiz with answers.

MCQs Introductory Statistics with Answers

A measure of dispersion is always
Which of these is a relative measure of dispersion
The measure of spread/dispersion is changed by a change of
Mean Deviation, Variance, and Standard Deviation of the values 4, 4, 4, 4, 4, 4 is
The mean deviation of the values, 18, 12, and 15 is
The sum of squares of deviation is least if measured from
The sum of squared deviations of a set of $n$ values from their mean is
Variance is always calculated from
The lowest value of variance can be
The variance of a constant is
Variance remains unchanged by the change of
$Var(2X+3)\,$ is
If $a$ and $b$ are two constants, then $Var(a + bX)\,$ is
Suppose for 40 observations, the variance is 50. If all the observations are increased by 20, the variance of these increased observations will be
Standard deviation is calculated from the Harmonic Mean (HM)
The variance of 5 numbers is 10. If each number is divided by 2, then the variance of new numbers is
If $X$ and $Y$ are independent then $SD(X-Y)$ is
If $Y=-8X-5$ and SD of $X$ is 3, then SD of $Y$ is
The standard deviation is always ———– than the mean deviation
If the standard deviation of the values 2, 4, 6, and 8 is 2.58, then the standard deviation of the values 4, 6, 8, and 10 is
For the symmetrical distribution, approximately 68% of the cases are included between
The percentage of values lies between $\overline{X}\pm 2 SD\,$ is
The measure of Dispersion can never be
If all values are the same then the measure of dispersion will be
The range of the values -5, -8, -10, 0, 6, 10 is

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Cohen Effect Size and Statistical Significance

May 24, 2024Apr 25, 2019 by Muhammad Imdad Ullah

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Statistical significance is important but not the most important consideration in evaluating the results. Because statistical significance tells only the likelihood (probability) that the observed results are due to chance alone. Considering the effect size when obtaining statistically significant results is important.

Effect size is a quantitative measure of some phenomenon. For example,

Correlation between two variables
The regression coefficients ($\beta_0, \beta_1, \beta_2$) for the regression model, for example, coefficients $\beta_1, \beta_2, \cdots$
The mean difference between two or more groups
The risk with which something happens

The effect size plays an important role in power analysis, sample size planning, and meta-analysis.

Since effect size indicates how strong (or important) our results are. Therefore, when you are reporting results about the statistical significance for an inferential test, the effect size should also be reported.

For the difference in means, the pooled standard deviation (also called combined standard deviation, obtained from pooled variance) is used to indicate the effect size.

The Cohen Effect Size for the Difference in Means

The effect size ($d$) for the difference in means by Cohen is

$d=\frac{mean\, of\, group\,1 – mean\,of\,group\,2}{SD_{pooled}}$

Cohen provided rough guidelines for interpreting the effect size.

If $d=0.2$, the effect size will be considered as small.

For $d=0.5$, the effect size will be medium.

and if $d=0.8$, the effect size is considered as large.

Note that statistical significance is not the same as the effect size. The statistical significance tells how likely it is that the result is due to chance, while effect size tells how important the result is.

Also note that the statistical-significance is not equal to economic, human, or scientific significance.

For the effect size of the dependent sample $t$-test, see the post-effect size for the dependent sample t-test

Cohen Effect size and statistical significance

See the short video on Effect Size and Statistical Significance

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Performing Chi Square test from Crosstabs in SPSS

Apr 7, 2024Apr 20, 2019 by Muhammad Imdad Ullah

Post Views: 50

In this post, we will learn about “performing Chi Square Test” in SPSS Statistics Software. For this purpose, from the ANALYSIS menu of SPSS, the crosstabs procedure in descriptive statistics is used to create contingency tables also known as two-way frequency tables, cross-tabulation, which describe the association between two categories of variables.

In a crosstab, the categories of one variable determine the rows of the contingency table, and the categories of the other variable determine the columns. The contingency table dimensions can be reported as $R\times C$, where $R$ is the number of categories for the row variables, and $C$ is the number of categories for the column variable. Additionally, a “square” crosstab is one in which the row and column variables have the same number of categories. Tables of dimensions $2 \times 2$, $3\times 3$, $4\times 4$, etc., are all square crosstab.

Performing Chi Square Test in SPSS

Let us start performing Chi Square test on cross-tabulation in SPSS, first, click Analysis from the main menu, then Descriptive Statistics, and then Crosstabs, as shown in the figure below

Performing Chi Square Test Crosstabs in SPSS

As an example, we are using the “satisf.sav” data file that is already available in the SPSS installation folder. Suppose, we are interested in finding the relationship between the “Shopping Frequency” and the “Made Purchase” variable. For this purpose, shift any one of the variables from the left pan to the right pan as row(s) and the other in the right pan as column(s). Here, we are taking “Shopping Frequency” as row(s) and “Made Purchase” as column(s) variables. Pressing OK will give the contingency table only.

The ROW(S) box is used to enter one or more variables to be used in the cross-table and Chi-Square statistics. Similarly, the COLUMNS(S) box is used to enter one or more variables to be used in the cross-table and Chi-Square statistics. Note At least one row and one column variable should be used.

The layer box is used when you need to find the association between three or more variables. When the layer variable is specified, the crosstab between the row and the column variables will be created at each level of the layer variable. You can have multiple layers of variables by specifying the first layer variable and then clicking next to specify the second layer variable. Alternatively, you can try out multiple variables as single layers at a time by putting them all in layer 1 of 1 box.

The STATISTICS button will lead to a dialog box that contains different inferential statistics for finding the association between categorical variables.

The CELL button will lead to a dialog box that controls which output is displayed in each crosstab cell, such as observed frequency, expected frequency, percentages, residuals, etc., as shown below.

Performing Chi Square test on the selected variables, click on the “Statistics” button and choose (tick) the option of “Chi-Square” from the top-left side of the dialog box shown below. Note the Chi-square check box must have a tick in it, otherwise only a cross-table will be displayed.

Press the “Continue” button and then the OK button. We will get output windows containing the cross-tabulation results in Chi-Square statistics as shown below

The Chi-Square results indicate an association between the categories of the “Sopping Frequency” variable and the “Made Purchase” variable since the p-value is smaller than say 0.01 level of significance.

For video lecture on Contingency Table and chi-square statistics, See the video lectures