#statistical test

Introduction: Hypothesis Testing Doesn’t Have to Be a Nightmare

If you’re a student just starting out with hypothesis testing in statistics you’ve probably had moments of frustration—especially when using SPSS or, worse, Minitab. Many students struggle with choosing the right test, interpreting output tables or even just setting up their data correctly. It’s not your fault—hypothesis testing can feel like a puzzle with too many pieces.

This is where SPSS help for students comes in. Unlike Minitab which can be overwhelming with its rigidity, SPSS is more user friendly. But even with SPSS things can get confusing. What’s the difference between a t-test and an ANOVA? How do you check assumptions? And what do all those numbers in the output window mean?

Don’t worry I’ve got your back. Below are 9 quick tips to make hypothesis testing in SPSS easier, faster and less stressful. Let’s get started!

1. Know Your Hypothesis Type Before You Touch SPSS

Before you even open SPSS make sure you clearly define your null (H₀) and alternative (H₁) hypotheses. This will determine the type of test you need. Here’s an example:

Null hypothesis (H₀): There is no difference in students’ test scores before and after using a study app.

Alternative hypothesis (H₁): Students score higher after using the study app.

If you’re not sure what type of test you need, SPSS has a helpful “Analyze” menu, but understanding your hypothesis is step one.

2. Choose the Right Statistical Test – It’s Easier Than You Think

One of the biggest struggles students face is choosing the right test. Here’s a quick guide:

If this is still overwhelming consider getting SPSS help for students from an expert—or if you’re really stuck you might even think, Can I pay someone to do my statistics homework? (Spoiler: Yes, you can, but learning it yourself is worth it!)

3. Always Check for Normality – Don’t Skip This Step!

Most hypothesis tests assume your data is normally distributed. To check normality in SPSS:

Click Analyze > Descriptive Statistics > Explore

Move your dependent variable into the Dependent List box

Click Plots, check Normality Plots with Tests, then hit OK

Look at the Shapiro-Wilk test—if p > 0.05, your data is normal. If not, consider a non-parametric test like the Mann-Whitney U test instead of a t-test.

4. Understand the p-Value – It’s More Than Just < 0.05

A p-value tells you to reject H₀, but students often misinterpret it. If p < 0.05 you have significant results (reject H₀). If p > 0.05 the results are not statistically significant (fail to reject H₀).

But here’s the catch: A p-value alone doesn’t tell you if your results are practically significant. Always look at effect size and confidence intervals for more.

5. Check Assumptions Before You Run Any Test

Most tests require assumptions, like homogeneity of variance (for t-tests and ANOVA). In SPSS you can check this using Levene’s test:

Click Analyze > Compare Means > One-Way ANOVA

Check the box for Homogeneity of variance test

If p < 0.05, variances are unequal, and you may need to adjust (like Welch’s test).

Don’t skip assumption checks or you’ll end up with wrong conclusions!

6. Use Graphs to Back Up Your Hypothesis Testing

Raw numbers are great, but SPSS’s graphs will make your results more impressive. Try these:

Boxplots for comparing groups

Histograms to check distributions

Scatterplots to see correlations

To create graphs in SPSS go to Graphs > Legacy Dialogs, select your chart type and customize to make your results more obvious.

7. Know When to Use One-Tailed vs. Two-Tailed

Many students assume two-tailed tests are always the way to go. Not true!

One-tailed test if you have a specific directional hypothesis (e.g. "higher", "lower")

Two-tailed test if you’re just testing for any difference.

One-tailed tests are more powerful but you might miss the opposite effect. Choose wisely!

8. Is Your Sample Size Big Enough?

Small sample sizes can lead to wrong results. Use G*Power (free) or SPSS’s power analysis to check if your sample size is sufficient.

Click Analyze > Power Analysis

Enter your effect size, alpha level and expected sample size

If your study is underpowered (if so you may need more participants)

9. Write Up Your Results Like a Pro (APA Style)

If you’re writing a report follow APA style. Here’s how to write up your results:

"An independent t-test was conducted to compare test scores between students who used the app and those who didn’t. The results were significant, t(48) = 2.34, p = 0.022, d = 0.65, app users scored higher.”

Always include the test type, degrees of freedom, test statistic, p-value and effect size.

Final Thoughts

This is the task of Week 1 of the course Data Analysis Tools at the Coursera Plataform. The challenge is to execute an Analysis of Variance using the ANOVA Statistical Test. This type of analysis assesses whether the means of two or more groups are statistically different from each other. Is used whenever you want to compare the means (quantitative variables) of groups (categorical variables). The null hypothesis is that there is no difference in the mean of the quantitative variable across groups (categorical variable), while the alternative is that there is a difference.

DataSet Used – Gap Minder Gapminder identifies systematic misconceptions about important global trends and proportions and uses reliable data to develop easy to understand teaching materials to rid people of their misconceptions. Gapminder is an independent Swedish foundation with no political, religious, or economic affiliations. should visit it: https://www.gapminder.org/.

The dataset used has 16 variables and 213 rows. I choosed to analyze income per person (incomeperperson) and life expectancy (lifeexpectancy).

And how is the Question?

Is the life expectancy different among four categories of income per person (A,B,C,D,E)?

Since the income per person is a quantitative variable, I transformed it into a categorical variable, using parameters sugested by IBGE to classify the social class of according of income. For the parameters, I analyzed the boxplot posted below.

the data in image is in portuguese, because the IBGE is an Brazilian institute.

The Code

I used the Anaconda to code in Python for this task. The code is posted below.

import numpy import pandas as pd import statsmodels.api as sm import statsmodels.formula.api as smf import statsmodels.stats.multicomp as multi import matplotlib.pyplot as plt import seaborn as sns import researchpy as rp import pycountry_convert as pc

df = pd.read_csv('gapminder.csv') df = df[['lifeexpectancy', 'incomeperperson']]

df['lifeexpectancy'] = df['lifeexpectancy'].apply(pd.to_numeric, errors='coerce') df['incomeperperson'] = df['incomeperperson'].apply(pd.to_numeric, errors='coerce')

def income_categories(row): if row["incomeperperson"]>15000: return "A" elif row["incomeperperson"]>5000: return "B" elif row["incomeperperson"]>3000: return "C" elif row["incomeperperson"]>1000: return "D" else: return "E"

df=df[(df['lifeexpectancy']>=1) & (df['lifeexpectancy']<=120) & (df['incomeperperson'] > 0) ]

df["Income_category"]=df.apply(income_categories, axis=1)

df = df[["Income_category","incomeperperson","lifeexpectancy"]].dropna()

df["Income_category"]=df.apply(income_categories, axis=1)

print (rp.summary_cont(df['lifeexpectancy']))

fig1, ax1 = plt.subplots() df_new = [df[df['Income_category']=='A']['lifeexpectancy'], df[df['Income_category']=='B']['lifeexpectancy'], df[df['Income_category']=='C']['lifeexpectancy'], df[df['Income_category']=='D']['lifeexpectancy'], df[df['Income_category']=='E']['lifeexpectancy']] ax1.set_title('life expectancy') ax1.boxplot(df_new) plt.show()

results = smf.ols('lifeexpectancy ~ C(Income_category)', data=df).fit() print (results.summary())

print ("Tukey") mc1 = multi.MultiComparison(df['lifeexpectancy'], df['Income_category']) print (mc1) res1 = mc1.tukeyhsd() print (res1.summary())

print ('means for for life expectancy by Income') m1= df.groupby('Income_category').mean() print (m1)

print ('Results') print ('standard deviations for life expectancy by Income') sd1 = df.groupby('Income_category').std() print (sd1)

Results – ANOVA Analysis

Aiming to answer the question of the task, I ran a test ANOVA. As shown below, from the 176 rows, 171 were used for the test, i have used a filter to remove some wrong values, as non numeric, negative, etc, reducing the rows of the original dataset

The ANOVA analysis shows a graph for each category (above) and, as we can see, the life expectancy of A class, have the life expectative of 80.39 years while the E class have the life expectative of 59.15 years.

by Fausto Keske

Introduction

This is the fourth and final assignment (Week 4) of the course Data Analysis Tools from the Wesleyan University at the Coursera Platform. Now, the challenge is to test a potential moderator. So, we are questioning whether there is an association between two constructs for different subgroups within the sample.

Case Study – Gap Minder

Gap Minder was founded in Stockholm by Ola, Anna and Hans Rosling. The company is a non-profit venture promoting sustainable global development and the achievement of the United Nations Millenium Development Goals. It seeks to increase the use and understanding of statistics about social, economic, and environmental development at local, national and global levels. Its website is mind blowing, everybody should visit it: https://www.gapminder.org/.

The dataset provided for this assignment has 16 variables and 213 observations. From the variables, I choose to analyze income per person (incomeperperson) and life expectancy (lifeexpectancy). The moderator is urban rate (urbanrate). The income per person is measured by the Gross Domestic Product per capita in constant 2.000 US$ (2010). And the life expectancy at birth (years) is the average number of years a newborn child would live if current mortality patterns were to stay the same. And the urban rate is % of total population that lives in urban areas (2008).

The Question

Are income per person and life expectancy associated for low urban rate countries? And income per person and life expectancy associated for high urban rate countries? In other words, our explanatory variable associated with our response variable, for each population sub-group? We are using a third variable to understand if this variable effects the direction and or strength of the relation between our explanatory and response variable.

To understand the two variables, I analyze the boxplots posted below.

Since urban rate is a quantitative variable, I had to transform it into a categorical variable. I created a sub-group for low urban rate countries and another one to a high urban rate countries.

The SAS Studio Code

For this assignment, I decided to code on SAS Studio, since the tool was new for me, and it was an opportunity to gain experience. The code is posted below. The comments are in Portuguese, my mother tongue.

Results – Pearson Correlation Coefficient (r) for both groups

Aiming to answer the question of the assignment, I ran a correlation procedure to obtain the Pearson Correlation Coefficient (r) for both groups. The results of the test showed a P value 0.0001. So, the test is valid, and we can analyze the results of the two sub-groups.

Since the r obtained is positive, we have a positive correlation between income per person and life expectancy for both groups. The correlation is stronger for the second group, the countries with higher urban rate. The r in this group is 0.63784. For the first group, the r obtained is 0.47392. These conclusions can also be seen in two the scatter plot posted below. We can see too much dispersion, when we display the points of the countries at the graph.

The r2 for the first sub-group (low urban rate) is 0.2246. The r2 is the fraction of the variability of one variable that can be predicted by the other. So, if we know the income per person, we can predict only 22.46% of the variability we will see in the rate of life expectancy.

by Fausto Keske

Introduction

This is the third assignment (Week 3) of the course Data Analysis Tools from the Wesleyan University at the Coursera Platform. Now, the challenge is to generate a Correlation Coefficient. This type of coefficient is used when you have two quantitative variables. For this assignment, as asked, I will use the Pearson Correlation Coefficient (r) that is a numerical measure of a linear relationship between two quantitative variables.

Case Study – Gap Minder

Gap Minder was founded in Stockholm by Ola, Anna and Hans Rosling. The company is a non-profit venture promoting sustainable global development and the achievement of the United Nations Millenium Development Goals. It seeks to increase the use and understanding of statistics about social, economic, and environmental development at local, national and global levels. Its website is mind blowing, everybody should visit it: https://www.gapminder.org/.

The dataset provided for this assignment has 16 variables and 213 observations. From the variables, I choose to analyze alcconsumption and lifeexpectancy. The alcohol consumption per adult (age 15+) is measured by how many liters recorded and estimated average alcohol consumption. And the life expectancy at birth (years) is the average number of years a newborn child would live if current mortality patterns were to stay the same.

The Question

Is there a correlation between alcohol consumption and life expectancy?

To understand the two variables, I analyze the boxplots posted below.

The SAS Studio Code

For this assignment, I decided to code on SAS Studio, since the tool was new for me, and it was an opportunity to gain experience. The code is posted below. The comments are in Portuguese, my mother tongue.

Results – Pearson Correlation Coefficient (r)

Aiming to answer the question of the assignment, I ran a correlation procedure to obtain the Pearson Correlation Coefficient (r). The results of the test showed a P value 0.0001. So, the test is valid, and we can analyze the results.

Since the r obtained is positive, we have a positive correlation between alcohol consumption and life expectancy. But this correlation is not strong, since our r is 0.31299, and the possible range is from -1 to +1. This conclusion can also be seen in the scatter plot posted below. We can see too much dispersion, when we display the points of the countries at the graph.

by Fausto Keske

Introduction

This is the second assignment (Week 2) of the course Data Analysis Tools from the Wesleyan University at the Coursera Platform. Now, the challenge is to run a Chi-Square Test of Independence. This type of analysis is used when you have two categorical variables. The null hypothesis is that there is no relationship between the two categorical variables, we can say that they are independent, while the alternative hypothesis is that there is a relationship between the two categorical variables, we can say that they are not independent. If your research question does not include a categorical variable, you can categorize one that is quantitative, which was the case of this assignment.

Case Study – Gap Minder

Gap Minder was founded in Stockholm by Ola, Anna and Hans Rosling. The company is a non-profit venture promoting sustainable global development and the achievement of the United Nations Millenium Development Goals. It seeks to increase the use and understanding of statistics about social, economic and environmental development at local, national and global levels. Its website is mind blowing, everybody should visit it: https://www.gapminder.org/.

The dataset provided for this assignment has 16 variables and 213 observations. From the variables, I choose to analyze employ rate (employrate), and suicide per 100.000 (suicideper100TH). The employ rate is a percentage of total population, age above 15, that has been employed during the given year. And the suicide per 100.000 is the mortality due to self-inflicted injury, per 100.000 standard population, age adjusted.

The Question

Is the employ rate and suicide per 100TH dependence independent or dependent?

Ho | There is no difference. Employ rate and suicide 100TH are independent.

Ha | There is a difference. Employ rate and suicide 100TH are not independent.

Since both variables are quantitative, I had to transform them into categorical variables. For the parameters, I analyze the boxplots posted below.

The SAS Studio Code

For this assignment, I decided to code on SAS Studio, since the tool was new for me, and it was an opportunity to learn it. The code is posted below. The comments are in Portuguese, my mother tongue.

Results – Statistical Test ANOVA

Aiming to answer the question of the assignment, I ran a statistical test Chi-Square. The results of the test showed a P value 0.0669. So, we reject the alternative hypothesis (Ha) and assume the Ho as true. So, we can get to the conclusion that there is no relationship between employ rate and suicide 100TH, they are independent.

If the P value were smaller than 0.05, we could accept the alternative hypothesis and say that employ rate and suicide 100TH are not independent. In that case, we should run a post hoc test for Chi Square tests of independence. Is this test we need to perform comparisons for each pair of employ rate across the three suicide per 100TH category. As part of the learning process, I ran the comparisons, and they are posted below.

Comparison1 (employ rate category 1 vs. employ rate category 2)

Comparison2 (employ rate category 1 vs. employ rate category 3)

Comparison3 (employ rate category 2 vs. employ rate category 3)

by Fausto Keske

Introduction

This is the first assignment (Week 1) of the course Data Analysis Tools from the Wesleyan University at the Coursera Plataform. The challenge is to run an Analysis of Variance using the Statistical Test ANOVA. This type of analysis assesses whether the means of two or more groups are statistically different from each other. It is used whenever you want to compare the means (quantitative variables) of groups (categorical variables). The null hypothesis is that there is no difference in the mean of the quantitative variable across groups (categorical variable), while the alternative is that there is a difference. If your research question does not include a categorical variable, you can categorize one that is quantitative, which was the case of this assignment.

Case Study – Gap Minder

Gap Minder was founded in Stockholm by Ola, Anna and Hans Rosling. The company is a non-profit venture promoting sustainable global development and the achievement of the United Nations Millenium Development Goals. It seeks to increase the use and understanding of statistics about social, economic and environmental development at local, national and global levels. Its website is mind blowing, everybody should visit it: https://www.gapminder.org/.

The dataset provided for this assignment has 16 variables and 213 observations. From the variables, I choose to analyze income per person (incomeperperson) and life expectancy (lifeexpectancy).

The Question

Is the life expectancy different among four categories of income per person (low income, average low income, average high income and high income)?

Ho | There is no difference. Life expectancy and income per person are not related.

Ha | There is a difference. Life expectancy and income per person are related.

Since the income per person is a quantitative variable, I had to transform it into a categorical variable. For the parameters, I analyzed the boxplot posted below.

The SAS Studio Code

For this assignment, I decided to code on SAS Studio, since the tool was new for me, and it was an opportunity to learn it. The code is posted below. The comments are in Portuguese, my mother tongue.

Results – Statistical Test ANOVA

Aiming to answer the question of the assignment, I ran a statistical test ANOVA. As shown below, from the 213 observations, 191 were used for the test.

The results of test showed that the F value is 57.93 and the P value 0.0001. So, we can accept the alternative hypothesis (Ha) and get to the conclusion that life expectancy and income per person are related. There are differences in the means of life expectancy among the four categories of income per person.

The ANOVA test also deliveries a boxplot for each category (below) and, as we can see, the life expectancy of the mean of the first category (low income) is 61.32 years. The 2 (average low) and 3 (average high) categories have 69.83 and 72.53 years of life expectancy. And the high category (4) has a mean of 79.49 years of life expectancy.

So far so good, we can determine that there are differences among the groups, but we can not tell which groups are different from the others. To obtain this answer, I applied the Duncan test, a post hoc test. The test showed (below) that the categories 2 and 3 are not significantly different, because they appeared at the same bar group. But we can see significant differences from the others in groups 1 (low income) and group 4 (high income).