2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

Let’s review the most common charts and graphs used in summary statistics.

Variable Type

Chart

Purpose

Summary Statistics

Pie chart or bar chart Comparative Bar Chart

One categorical Two categorical One scale

Show frequencies, or proportions, or percentages Compares proportions within groups

Class percentages

Percentages within groups

Histogram

Display data distribution

Mean and standard deviation (will normally show a box plot with it)

Box plot

One scale/one categorical Two scale

Compares spread of values

Median and IQR

Scatterplot

Investigate relationships between 2 variables and helps detect outliers Used to see if mean varies between different groups of data

Correlation coefficient

Line chart

Scale by time Investigate trends over time

Means by time point

Means plot*

One scale/2 categorical

Means

Table 107: Use charts for specific variable types and purpose

We are getting closer to diving into answering, “What test should I use?” Remember that your test will depend on whether the data is normally distributed (parametric test) or ordinal/skewed data (non-parametric test). Normally, you visualize the data through graphs, but you can also test normality using numerical tests. The tests for assessment of normality include the Kolmogorov-Smirnov test, the Lilliefors corrected test, the Shapiro-Wilk test and several others. To test for normality in SPSS, use Normality Tests: Normality tests are supplementary to the graphical assessment of normality. If you are unsure of how to interpret box plots, confidence interval, or histograms, you can run a normality test in any of the statistical software. It is usually located in the exploration (for example in SPSS: Analyze> Descriptive Statistics > Explore > Plots>Normality plots with tests (checkbox) Essentially, look for “normality plots with tests” The illustration (from SPSS version 27) shows Kolmogorov-Smirnov (K-S) test and the Shapiro-Wilk test. Most researchers recommend the Shapiro-Wilk test as the best choice. “ The Shapiro-Wilk test is based on the correlation between the data and the corresponding normal scores and provides better power than the K-S test even after the Lilliefors correction ” (Ghasemi & Zahediasl, 2012). The null hypothesis for a normality plot test is that the “sample distribution is normal.” If the significance column exceeds .05, you do not reject the null hypothesis and you have met the assumption of NORMALITY (or normal distribution of the dependent variable).

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